Great city, easy to use transport links, plenty to see and do and as a geography lesson joebhoy is it on the estuary of the Tagus, a river, not on the sea coast, the Vasco de Gama is the second longest bridge in Europe and is across that river. The oldest part of the city is called the Alfama which is a twisty, narrow-streeted area build on the hill which is topped by the Castel de St Jorge, thoughtfully rebuilt by Salazar). Beside that is Baixa (where Rossio is) and Avenida, this part of the city is lower and flatter and was laid out in a grid pattern after the 1755 earthquake and is a very pleasant quarter, next to that is Bairro Alto which (as the name says) is another steep hill with more narrow winding streets and is an area filled with traditional Portugeuse bars and restaurants. Any of those three areas will put you in the centre, they encomapss a fairly tight area and are easily accessible from each other. I would suggest though your best bet would be to look at hotels near to
Metro stations since this will make it easier for you to get around to the different areas (each trip costs €0.80) it expands the selection of hotels (There is a stop in Rossio and it is about as central as you can get!). Metro smart cards cost €0.50 and are dispensed by the ticket machines in the stations, you can easily charge them and the machines have an English language option. They can also be used on the buses.
I'd second all of Galwegian's suggestions and I'd add the Elavador de Santa Justa and at least one of the funiculars. There is also a tram system and there are old fashioned and newer trams, one of the old fashioned routes is out to Belém and another winds up the hill to the Castel de St Jorge (from which the view is stunning). I'd visit the Camera Obscura in the castle by the way - especially if you have children, it is fascinating. Cascais is just over half an hour by train from Cais De Sodré, there is also a lovely beach at Estoril which is a couple of stops before it. You should try to a wine tour, I did the one at the vineyard of José Marie de Fonseca in Azeitao (Fertagus to Coina and 2N bus to Azeitao, it terminates about a minutes walk from the vineyard). I'd also recommend taking a trip on one of the ferries to get a different perspective on the city, they depart from two terminals in Lisbon (Cais de Sodré and I can't recall the name of the other) and the terminal in Belém.
One thing I found puzzling is that while the smart card works on the Metro and the
bus without any bother, I had to get an almost identical smart card each for the
Fertagus, the
trains and the
ferries - it gets a little confusing! (Some of those sites have an English language version)
Oh and wear a decent pair of walking sandals because all that pretty stone paving is rather hard on the feet, legs and back!