For daytrips, consider Coimbra, a 15th Century University town an hour or so north of Lisbon; and Tomar, which also has a lot of history.
Then you have Estoril, Cascais and Sintra along the coast.

If you plan to get 'off the beaten track' you should have a Portuguese phrasebook to help you communicate. Surprisingly, many people in Lisbon know some rudimentary English and the young ones are happy to try it out on an English-speaker.

Sintra (the old town part) is gorgeous; the Castle of the Moors, Pena Palace, and the Capuchin Monastery are all parts that I loved. (I stayed in Sintra and visited Lisbon, actually; lovely mountain weather.) I'd recommend this for your overnight, as it can be a bit crowded during the day, but much more relaxed and lovely at night.

Cabo da Roca was very enjoyable for me, as a bit of a geography geek: the westernmost point. It's quite picturesque.

Obidos, the medieval city, was another good day trip for me.

I was in Portugal for two weeks (including three days in Madeira) and was just in the general Sintra-to-Lisbon region; I had no problems getting around on public transportation, even without speaking Portuguese. There were lovely older ladies who managed to direct me whenever they saw me looking confused! (My permanent sense of direction state, some would say...)

Don't forget to have some Serra cheese. MMmmmmmm.

Hi; You mentioned an 'overnight'. With eleven day you could consider five days in Lisbon and six days in the countryside. Driving is easy. Fly into Lisbon, hire a car and go to the Parador in Estremoz for three days. There is so much to see in that area. One day go to Evora and Monsaraz. Another day there is Elvas and Villa Vicosa to visit. Then on to the Parador in Obidos for three days. On the way visit Marvao. In this area as Amy and Ned have suggested, many places to visit. There are major highways to drive to these places. Tomar,[huge Convento, lovely town] Fatima,[basilica] Batalha,[abbey] Alcobaca, [huge church] Leria, [lovely city] Nazare, [fishing village and great beach] and Combria, [wonderful city]. Then just outside of Lisbon you have Sinta. Just north of Sintra there is a great Palace called Mafra. After six days in the countryside, drop the car at the airport and spend your last five days in Lisbon. Dick

What Iris said, but maybe in reverse order depending on where you are coming from. Lisbon is a good place to recover from jet lag.

We stayed a couple of nights in Batalha and found it to be a good base. We visited Fatima, Tomar, Nazare and Ourem from this location. Our room at Casa do Outeiro had a marvellous view of the abbey - really beautiful when lit up at night.

However, for day trips, Sintra / Cascais / Cabo da Roca and Evora are all very good.

You can travel by train and bus if you don't want to drive. I loved Lisbon, Belem and Sintra, but the north is also worth visiting if you have 11 days. My TR for Lisbon is http://www.fodors.com/community/europe/loving-lisbon.cfm?34 and for the north (includes Coimbra and Obidos) is at www.wilhelmswords.com/rtw2004.

Are you tied to Lisbon because of a rental there? If not, I would spend a few days in Lisbon and then travel around the country by car. The only area I have explored beyond Lisbon is the Alentejo, which we enjoyed so much in our two days that we would like to go back some time for a week.

utrechtman:

About a year ago (April-May 2008) we did somewhat what Nikki describes above (we are members of the Prestigious Lobo Lisbon Appreciation League..inside joke, sorry)...started out with five days in Lisbon (don't give it short shrift..a delightfully interesting city)...we ventured on by rental car to the pousada in Arraiolos, also visited Evora and several other Alentejo towns, made our way to the scenic
Marvao pousada mountaintop on the Spanish border, then on into the Serras for a stay at the Belmonte Pousada, afterwhich we went on to colorful Obidos (oo-bee-doosh) while day tripping to oceanside Nazare' and it's upper level Sitio section...ending up in Sintra whle including it's sites, and also Cabo da Rocha, Cascais, Estoril...
...here are my pics which perhaps will give you an insight into possible choices in that "gem of a country".. don't sweat the language..very few visitors aside from Brazilians speak Portuguese...you'll get by fine..and the driving is very easy, well-marked roads, etc.

Whatver you decide, you will love Portugal...I promise and I'm sure Nikki and Lobo will join me in that!

Stu Tower

http://picasaweb.google.com/stuarttower/Portugal2008#

Use "slide show", sit back and relax.

note:

If any of you is older than 55 , get the Golden rate for Pousada lodging...about 40% off published rates...quite a coup, once you see some of the magnificent pousadas.
stu

Am I missing something? I know Aparador is a pencil sharpener, but never heard the word Parador.

I think maybe the best way to see the Alentejo countryside is by car.
Lobo: Maybe with Parador they were getting mixed up with Spain?

ok, maybe that's the explanation I can't help since I don't speak Spanish. I'll ask Loba later today
Nikki, we are waiting 4 you. Please come.

STu Tower: I'm glad you were featured this week in Fodor's, as I went and looked at your wonderful photos of Portugal.
Utrechtman: Every thing said in the above replies has merit. It is a wonderful country, where we have visited three times in the last 25 years.
The first time we drove up an inland route to Tomar, Viseu, Lamego, then Guimarais, Ponte de Lima, and ending in Valenca da Minho, and it was heavenly. No tourists, just beautiful manueline architecture, lovely welcoming pousadas, esp. in Valenca da Minho, where they were rebuilding the cobbled street, and we watched mesmerized.
there is more to see, and I want to go back now that I have been reading about Lobo Mau and the Lisbon GTG's

Lobo. Can I come too?

Sher

Sher, message for you in "Lisbon inside tips".
Taconic, I retired from GTGs for the benefit of my waistline I'll return to the active only for Sher or Nikki (or both).

Stu; Great photos. Soon I hope to be able to put some of mine on-line. Need my sister to help. Dick

Lobo. That is really nice of you. We are seriously thinking of it although I had decided to swear off Europe this year.

Now. To convince Mr. Sher.

STu Tower: I'm glad you were featured this week in Fodor's

Hi Taconic:Huh?I know nothing about this..please enlighten me.
Thanks..

Utrechtman: Another tip..go to the thread that Lobo suggests a few posts above...there you will get a ton of tips

stu tower

Stu - www.fodors.com/newsletter - you can sign up to have it sent to you by email.

We spent time in both Sintra and Lisbon, with a day trip to Cascais and Belem. Lisbon is great for good food and night life and fado music. Don't miss riding the street car through the Alfama area or the famous cakes from Belem or the porto wine.

WE used public transportation to go to Sintra and had no problem even though we do not speak Portuguese. Absolutely loved Sintra and the tours tours through the palaces. It is a much more relaxed pace than Lisbon with nice small shops with lovely ceramics. After leaving Sintra we returned by train just to buy a lovely ceramic rooster that struck our eye.

thanks all for your responses. you've given me good trip-planing info. they are very helpful. Nice pics Stu!!

Thanks, KMW...I didn't even know there was a newsletter...
and thanks for the heads up, Taconic...now I can tell my publishers that Fodors will be in competition for my next book (LOL)...

stu rozstu1@aol.com

Anybody been to the Algarve in the winter for a budget holiday?

Hi ..
I would like to share my experience when i went to Spain earlier this year for my honeymoon, we spent about a week in southern Spain, two nights in Sevilla. We didn't do much in Sevilla beside the cathedral and alcazar, but there are a lot of places around outside of town. One thing - get a good map of Sevilla, as it's a nightmare to drive through, especially if you're trying to start from anywhere in the old part of town.
One of our favorite towns in Spain was Tarifa, right at the Southern tip. It's like a little California beach town. If you want, you can catch a ferry to go to Morrocco from there.

Granda might be a little out of your of your driving range, but is a gorgeous town, and the Alhambra is amazing. We spent 6 hours there. If you at all plan to go, get your tickets beforehand from ServiCaixa, and pick them up at one of the electronic will-call booths at the front gate - it's really simple, and the place only allows 6000 people in per day, so you risk not getting in if you're going during a time that's at all busy. The audio tour is worth it...
there was lot more.