Weather may be the easiest party to answer. April is great, May can be very good, June OK or can be hot, July August September hot, October nice again November through March is rainy season so you could get many nice days in parts of the country, but cool and rainy is a definitely reality.

The complications set in when you realize that the nicest times may also coincide with major Jewish holidays. The prices of airfare and hotels go way way up, availability goes down, many places are extremely crowded and public transportation and some sites are closed extra days for the holidays.

So if you can go right before or after the major religious holidays in Spring or Fall, you can get some of the best combinations of weather and reasonable time to travel
Passover is April 14 - 21, 2014
Rosh Hashana September 24 - 26, 2014
Yom Kippur October 3 - 4, 2014 , 2014
Sukkot October 8 - 16, 2014

May has 2 other days that could affect your trip
Memorial Day May 5th (which unlike in the US is observed as a solemn day) and then Yom Ha'atzmaut (independence day)May 6th 2014, They are not religious holidays but there are restrictions,observances and celebrations that will be important to note.

The other details--well, for how long would you be in Israel? Do you generally travel independenly? Driving or public transportation? Most importanly , what are your interests--archaelogy, religious sites (Jewish, Christian, Muslim?), beaches, hiking, art, food? There's so much to do in Israel and how much time you need and where to spend your time depends on your priorities.
Some people love to hang out in Tel Aviv for the beaches,clubs, restaurants etc and some think it's just like being in Miami and would rather skip it.

Thanks so much AlexaA. That is really really helpful.

We would likely travel for 10-12 days. We generally travel independently, but hire single-day guides for cities/sights. We sort of like a mix----art and history for half, ending with beaches and physical activity. We are foodies and will try anything once. Yes---I have heard the pros and cons of Tel Aviv---but its location could make a handy base for side trips.

Your questioned asked if November or May was better. Early November and May are pretty similar. There is a slim slim chance of a small amount of rain in NOvember, but you have a better chance of it being hot!

If you are going to be in Israel for 10-12 days than you definitely need more than one base. You need to base in Jerusalem, Obviously you will be spending time in Eilat. If you plan on going North ( and you have the time) to visit the Galilee you should stay up there. For Tel Aviv and Jerusalem you neither need nor want a car. The Dead Sea /Masada is a day trip from Jerusalem. A car is nice and you could, if you want, continue to drive South to Eilat. After Eilat and Petra you could either take a bus or fly north again. A rental ( or driving guide) is definitely needed when touring in the North.

I don't know what "cons" there are for Tel-Aviv : It was selected as one of the world's top 10 beach cities by National Geographic, it has excellent museums, historical sites (Jaffa), markets, culture and restaurants. The only "con" is that other more unique and significant places have a higher priority for a short visit - Jerusalem, Dead Sea, etc - but that is hardly Tel-Aviv's fault !

Thanks so much for your information everyone. I did have one follow up question. Is is practical/efficient to use Tel-Aviv as a base and travel to the Dead Sea or Jerusalem during the day? The reason I am asking is my husband has A LOT of hotel points for a major hotel in Tel-Aviv.

2) What is readers' honest opinion on Eilat? We are considering Eilat due to the fact that we are scuba divers and Eilat is a convenient jump off point to Petra. I know previous reviewers say Egypt Red Sea diving is superior (I've been---it is pretty incredible). Is the vibe in Eilat similar to Sharm-el-Sheikh?

I would prefer Aqaba over Eilat - prettier town, better hotels, better beaches and you reach Petra better because you already behind the border. We did only snorkeling - but enjoyed it very much. Lots of coral reefs just meters from the beach.

We like the Marina Plaza Hotel.

I assume that you want to spend more than one day in Jerusalem. The bus service between the two cities is excellent and cheap (18 NIS). Buses leave every 15-20 minutes from the Tel-Aviv Central Bus station (#405) or from the Arlozorov Terminal in north Tel-Aviv (#480 - **recommended**) and go to the Jerusalem CBS. The trip takes about an hour, but you have to add about 30 minutes from the hotel to the station, i.e. you will spend about 3 hours traveling every day ! If you want to go to the Dead Sea from Tel-Aviv you will have to drive through Jerusalem anyway. In short.pend at least 2 nights in Jerusalem.

Tel-Aviv is Tel-Aviv, a city in Israel but not very distinctive nor historical. There are some good museums and hotels and restaurants and very good shopping.
Jerusalem is Israel, historical, biblical, Jewish, Palestinian.
You do not go there just to see things, although there is so much to see that you will need at least 2 weeks. You immerse yourself in Jerusalem and get to feel israel. You will want to come back whether you are Jewish or Christian.
You will do yourself an injustice if you only spend a day or two in Jerusalem and only visit for the day.

Hi: as an expat in Jerusalem who travels around a lot, I wanted to weigh in on your questions. Definately plan on staying in Jerusalem for several days/nights. Just exploring the Old City will take 1-2 days and there are other sites around town you will want to consider seeing like the Dome of the Rock, Mt Scopus, Holocaust and Israel museums.
Consider staying at the YMCA hotel [in West Jersualem ]for it's fab location near the Old City. It has a lovely terrace [non kosher] restaurant or other Chain types like the David Citadel are also close. Mind the local holidays --there are many--as they will bring in crowds and increase prices, like the upcoming Easter/passover. May is a lovely time to be here.November was nice but can be rainy.
Next: tel aviv is a very fun town where you can hang on the beach and have some hummous and falafel and watch the locals play paddle ball or surf. We get there [with our 3 kids] as often as possible for non-kosher food and a carefree vibe. Jerusalem is very intense and having most places closed on friday nights and all day saturdays can be a drag.Strolling along to Jaffa is also lovely and there are various sea food places as well. [Manta ray]
Also: and most importantly: tel aviv is a good base to explore some places further afield although if you are planning on going North to Galilee/Golan or coastal sites like Acco/akko/acre or Cesearea it may be best to rent a car and stay closer to those sites. Some can be done from TA however.
Eilat: we have been here almost 3 years and have considered going to Eilat, but have driven right past it to the Jordanian border and gone to the Aquaba area 5 times or so. Eilat is known to be very built up, crowded and lacking charm. You can see that just by the fast-food places all over the place. It is also pricey for what you get. Hotels in general are very pricey in Israel.
Anyway, you can get a visa and walk through the border [and leave a rental car at the border if you have one as you can't bring cars with Israeli plates through.] Anyay, there are taxis to bring you to the beaches/hotels in Aquaba. A mile or two down from Aquaba is Tala Bay and that is where we go for very nice resorts at good prices and fab service. Anyway, if you are planning on going to Jordan than you must do Petra. Petra is an hour or more from Aquaba. My inlaws rented a taxi at that border and took it right to Petra. You can also arrange this type of trip at an agency located at the main gate in the Old City-jaffa gate in JERS. They do bus trips.
They could also arrange bus trips to Masada/Dead sea if you wnt to do just a day trip there. Anwyay, I could go but hope that helps a bit.

I have to disagree with some of the comments in the post above. While much is closed in Jerusalem on the Sabbath there is also plenty to do if you end up there on that day. The Old City ( except for the Jewish Quarter) is 100% open. The Israel Museum, the Tower of David Museum, the zoo--all are open. There are also an increasing number of non-Kosher restaurants in Jerusalem. Finally, the municipality always offers a free walking tour or two on the Sabbath.

Saturday is also a good day to take a day trip to Masada or a 1/2 day trip to Bethlehem.

Yes, of course there are some things open. You mentioned some good ones above as well as the zoo, Ein Kerem, of course Bethlehem etc And a few restaurants, which I can gladly name in Jerusalem proper. But, they are usually super packed with locals, and when one lives here--as maybe you do too--you can only do so many of those without wanting to venture out of Jerusalem and exploring a vibrant city, like TA which is thriving on Saturday. That is all I was referring to. ENjoy your trip planning!

So if Tel-Aviv is "thriving on Saturday" then it must also be "super packed with locals". Anyway, the person asking the question is a tourist who wants to visit Jerusalem and there is more than enough to do there on a Saturday to keep any tourist occupied (see the list posted by Elkaz). Note that most of tehmuseums in Tel-Aviv are NOT open on Saturdays either.

I agree with the above posters that Jersualem deserves more time than just a day or two. And if you were going to stay in Tel Aviv to get to Jerusalem (assuming more than once) it would be a real commute, not what I'd want for my vacation

Yes, Tel Aviv is central enough for a base if you want just single trips to other places. You wouldn't want to explore much of the north from a Tel Aviv base. It's not a huge country, but the traffic can really make things less than ideal. I've done Masada as a day trip from the Tel Aviv area because it was my only chance on that trip, but it wasn't fun. I didn't go through Jerusalem , by the way, but came through Arad. If you were going to walk up and down to Masada, that is actually a shorter way from Tel Aviv. If you plan to use the cable car up or down and see Ein Gedi or other Dead Sea sites--well, it was a very long and tiring day!

About the Jerusalem on Saturday debate, in my opinion there are better ways to use your time. Years ago, literally nothing was open. I know that much has changed, but you still would have to do more planning than on another day of the week. Lack of public transportation is a pain, and frankly I like to visit a place when virtually everything is open, not just a restaurant here and there and some sites. I want to be able to stop and get a snack or a drink somewhere without having to plot out what's open! Some people want the special Shabbat atmosphere in many places in Jerusalem, but some don't and will feel restricted in the areas you can drive through, or see and visit.

If you have a car and are somewhere other than Jerusalem, your options are greatly increased.