Budget:
You will find traditional meals served in small coffeeshops/restaurants, especially in the old parts of town. Some will be better than others, just check if there are a lot of locals eating there! They will be very cheap (as low as ?5 for a full meal) and home-style cooking. The owners probably wont speak english and the menu will probably be in portuguese only!
Café Buenos Aires: Calçada Escadinhas do Duque No. 31. A good and selected combination of cheap and mid range dishes. The owners are very friendly and speak English, as well as Portuguese. (This restaurant would not be described as budget by any Lisboeta that I know or have known! It is a good restaurant if you want to eat south american grilled meat in Lisbon.)
Gurkha: Arco das Portas do Mar, 9 (Near Casa dos Bicos). Among Lisbon's many curry houses, this Nepalese restaurant is a little hidden, but offers good value Asian food (tandoori, curries) for a total of about about 8-12 euros per person.
Mid-range:
Alfama:
A Tasquinha: (from donwtown, turn left near Igreja de Santa Luzia to Rua do Limoeiro; then turn right to Rua de Santiago. Pass Camidas de Santiago. Look for outdoor red chairs and tables, white umbrellas), Largo Contador Mor 5/7. Great food; owner and guest signers perform fado on Fri evenings without charging extra for it; many outdoor tables; great red Sangria. Try bacalau with potatoes and onion in cream sauce excellent change from ubiquitous "rice/chips with grilled everything".
Chapito: Dinner: from 7:30pm. Great views are the main feature if you reserve terrace seat in advance. Good atmosphere; international-menu food is tasty but nothing special.
Chiado:
Cervejaria da Trindade: R. Nova da Trindade 20C (Chiado neighbourhood). Everyday : 10AM-1:30AM. Excellent restaurant-brewery that has several kinds of Sagres beer and also Guinness. Beware with the appetizer that is charged for each item that is consumed separately. Nice codfish plates. ?15-25.
Bairro Alto:
Terra: Rua da Palmeira 15 (near Jardim do Príncipe Real). Probably the best vegetarian restaurant in Lisbon and also the nicest in terms of ambience and service. They have a menu in English and will help with vegan choices or people with other dietary restrictions. Reservations are recommended, especially on weekends but you will always be served even if you arrive with the place full and have to wait for a while. Weather permitting try to get a table "outside", which means a wonderful and secluded back terrace. ?15-20 (Vegetarian Buffet plus drink and/or dessert).
Splurge:
Eleven: Rua Marquês da Fronteira. If you really feel like splurging, this is the place. The restaurant was recently awarded a Michelin Star, although the basis on which the award was made are disputable.
Il Gattopardo: Av. Eng. Duarte Pacheco, 24 (3rd Floor of the Dom Pedro Palace hotel). Lunch: 12:20PM - 3:30PM, Dinner: 7:30PM-11:30PM. An elegant restaurant serving fashionable gourmet Italian with a big price tag.