To stay: VIP Eden on Praca dos Restauradores has a great location, views from the higher-up rooms are fabulous, and from the rooftop breakfast terrace. More an apart-hotel, you get a mini-kitchenette with fridge, microwave and so on, and a balcony.
Not to miss: the Port Institute in the Bairro Alto; Sintra for a day-trip (UNESCO heritage site, Palacio Nacionale, Moorish castle, most terrifying busride ever from the town up to the castle - close your eyes); in Lisbon itself, don't miss taking one of the funiculars - there's one right by the VIP Eden up to the Bairro Alto, and it's handy for the Port Institute!
Other things / places: Cascais, a tram ride (or a long walk - whatever takes your fancy!) down the coast, has a fortress and a few other points of interest, and neighbouring Estoril has a famous casino (as in Casino Royale). The Expo 98 site is now called the Nations Park - the only thing really worth going to there is the Aquarium, but it's surprisingly good: not your usual few depressed looking carp.
Lovely city - but you only need to try bacalhau (salt cod... and by hell it's salty) once, and while you can eat very cheaply, it can be worth splashing out.