Diamantina

International Design Hotel has a great, convenient location at Rossio Square, so you're near Rossio Train Station, where you can catch the train to Sintra, and close to the Praça de Figueira, where you can catch the Tram 15 to Belém. See:
http://lisbon-portugal-guide.com/lis...-15-route.html
There's also a metro station at Rossio Square.
Plus, it's not on a hill!
This link will tell you more about Baixa:
http://www.golisbon.com/sight-seeing/baixa.html

You won't be driving in Lisbon, correct? Not necessary, as the public transport system and taxis are convenient and cheap. You'll have to watch out for pickpockets on some of the trams, especially Route 28, which is convenient for getting to the Castelo de São Jorge. Please don't let my warning put you off taking this historic, scenic-route tram, but do be aware of your surroundings and the people around you; the pickpockets work in groups. I wore a money belt under my clothes and carried a PacSafe shoulder bag (reinforced with wires), so I wasn't too worried.

We considered staying at International Design Hotel as it gets great reviews on Trip Advisor, but we ended up staying on Avenida Liberdade, near the Avenida metro station instead, because this area looked less busy, but still convenient.

On our last trip to Lisbon in September 2015, we stayed in a hotel near Avenida Liberdade at the beginning of our trip, traveled to Andalucia and the Algarve, then returned to Lisbon for a couple of nights before catching our flight to the U.S. On our return to Lisbon, we stayed at a hotel near Parque das Nações. Normally, I wouldn't recommend staying here, as this area is far from the center and new (rather than historic), but it is close to the metro and train, restaurants, a shopping mall, and the Oceanarium, one of Europe's best aquariums. Our hotel also had a free shuttle to and from the airport.

Diamantina

Here are links to more info about Lisbon's trams:
http://www.lisbonlux.com/lisbon-tran...lectricos.html
http://lisbon-portugal-guide.com/lis...ram-guide.html

martu518

Thank you, thank you! Your input is highly appreciated. I'll start by saying, yes, we have booked our tickets and are arriving and departing from Lisbon. I am waiting to hear from the Bairro Alto Hotel in Lisbon (great reviews) - we have a couple more options and will decide on one of them this weekend. I also need to check the hotels you have provided me.
Diamantina, you're right, we are not planning on driving while in Lisbon.
PalenQ, we're trying to decide between Obidos and Evora. It's been difficult to figure out how many days we should dedicate to Andalucia.
MyriamC, been reading about the Amadeus, what did you like most about it? I definitely need to do a little more reading tonight and tomorrow. Thank you all again! Martu

MyriamC

Amadeus:
1) location!, especially being near a parking garage because we only take a small carry-on with us in the hotel and leave our 'big' luggage in the trunk of the car when we are 'en route'.
2) it's on a quiet pedestrian street. I am very sensitive to noise (and light).
3) music is the hotel theme and all the communal rooms have musical instruments that can be used by the guests. I can still hear the private piano recital that was played one night by a guest.
4) they do an excellent breakfast that can be taken on the rooftop terrace with great views.