Campo de Ourique, my first choice (and where I live with my family)! Cool and friendly neighborhood, lots of people on the street, small cozy shops, lots of good restaurants, very safe, 5 minutes from the centre, 10 minutes from the places to go out at night, 5 minutes from the highway to go to Cascais or to Costa da Caparica (beaches), plain neighborhood to walk or to ride a bike... the best!

I spent a month in Mouraria, not far from the Martim Moniz metro stop. The area is really interesting. When Lisbon was hit by an earthquake, tsunami, and then a fire in 1755, much of the city went up in flames. Mouraria had many buildings that were unscathed. It's thus older in feel, with narrow lanes and tiny restaurants with no names. It also houses an immigrant population that you don't feel as much elsewhere in the city, which was part of why I wanted to live there. With restaurants like Jesus é Goês and Restaurante Zé da Mouraria and Restaurante Cantinho do Aziz and The Food Temple, it's also a really interesting place to eat because it gives you a chance to sample not just great Portuguese food, but also amazingly authentic ethnic eats.

A lot of friends enjoyed Alfama (they were not far from the Memmo Alfama Hotel Lisboa). It's fun for a few days but I found it too touristy -- not in the shops/attractions, but literally there were just too many tourists milling about. In contrast, Mouraria really felt like a neighbourhood. Hope this helps!

It's not easy to rent for 3 months, but I would advice Saldanha, Campo Grande, Lapa, Campolide or Restelo. If you want anything really on the downtown, Bairro Alto, but would not advice it.

Let me know if you want to meet any other cities around here like Aveiro, Porto, Faro, etc :)

Though I am hopefully going to be living here permanently, I know some people who rent short term places (I am currently in a 3 month place, until my visa is completed). So it's not too hard to find short term. As for living, I like Palacete de São Bento or Santos, both fairly central and a short walk to everything fun, but far enough away to be quiet at night. Also, Marquês Pombal and Sao Sebastio. They are a little farther out, but not really far at all, and a little cheaper since they are not central. Anjos, Intendente, Martim Moniz will offer a little more ethnic diversity and maybe even more cost effective, and also off a metro line direct to the center.

To stay in downtown near everything but in a quiet, centric and very real neighborhood check Centro Comercial Mouraria (Mouraria) in the Castle's hill.

Baixa and Chiado are popular neighborhoods in Lisbon. Bairro Alto has a great restaurant and bar scene but can get kind of dangerous at night.