Is 2 days going to be enough time for Athens. We would like to visit the Acropolis, Acropolis Museum, Ancient Agora and the National Arch. Museum.

OOps, forgot the Parthenon

That is enough time but as third day would give you more time for the Central market, Hadrians Library and just wandering around the fascinating Monestraki and Plaka areas.

Two days is plenty of time if both of them are whole days and you can do a lot of walking. Be prepared to go up and down hills.

I recommend doing the Acropolis and the ancient Agora on the first day. (The Parthenon is the big temple ruin on the top of the Acropolis.) They are close together and will set up the feel for ancient Greece.

The Acropolis Museum is good but not a "must see" compared to the National. And it's on the south side of the Acropolis, other side from Monastiraki. But if you do have have enough time and energy the entrance to the museum with its glass paving over an old excavation is interesting. The Temple of Olympian Zeus and Hadrian's Arch are only a couple of blocks from there and also fun.

Monastiraki Square is in front of the Acropolis and the center of things. There are a lot of restaurants in the area. Ermou Street from Monastiraki Square up to Syntagma Square is a fun walk after dinner. Hadrian's Library is near by and OK if you happen to pass it.

Start the second day with the National Archeological Museum. It's north of central Athens but an easy metro ride (Omonia station plus a 10 minute walk). Spend a couple of hours there then wander back to the center and spend as much time as you want in the Monastiraki area and markets.

Nightlife in the Plaka is something else. But I'd stay out of it unless you're with someone who knows their way around. Very crowded and very confusing.

Go to the Parthenon when it first opens in the morning to avoid the crowds and organized bus tours, and to get a much better sense of it. The new Acropolis Museum is fantastic. There's also an excellent restaurant there where you can sit and recharge before moving on to the Agora. Save the NAM for your second day. It's amazing in its scope, and takes hours to explore. Wear good shoes!

2 days is enough for what you have stated you want to do, but for the city as a whole & its host of other sites, no it's not enough.
Many love Athens & return again & again as there is always more to do, those that say 1 or 2 days is enough generally have not seen much & not given themselves time to explore properly. As you wander around it is very easy to get sidetracked as you spot something else!
After approx 30 visits & now living here for 3.5 years I am still finding different areas to explore & revisit some places more than once
Whatever you do though, a big factor in enjoying your visit is the hotel you choose & its location. Have you already got one in mind?

We spent three days on first visit to Athens but increased it to four on our second trip. Your list is of the top sites but there are so many palaces to explore, neighborhoods also Cycladic Museum, Benaki Museum, Lycabettus hill, take a food walking tour,Olympic Stadiums, old and recent ones. etc.

I have not even begun to think about a hotel yet, do you have any suggestions?

tidy, to avoid wasting our time and yours with listing hotels that don't meet your criteria, please give us your desired budget range (in Euros please, many of the contributors here are not from US) -- here's a conversion site: http://www.xe.com/currencyconverter/ -- it will also be super-helpful if yo can remind us of the exact 2 days you have in mind.

For us, the National Archaeology Museum took an entire day. There's a cafe onsite so you can take a lunch break!

We also found the new Acropolis Museum to be fantastic and very moving.

A small museum favorite is the Goulandris Museum. The Benaki Museum
is also amazing.