I'm going to be in Lisbon next month and will be on a pretty tight budget. I'm looking for the best free and inexpensive things to check out! I love the outdoors, art, museums, you name it. Thanks!
The best thing to do in Lisbon is to walk and walk, exploring the city from its many vantage points. Weave in and out of the touristy areas as you go, climbing to Miradouro da Senhora do Monte, then looping back down toward the sea near the Mercado da Ribeira. Walk around Alfama, stopping in at the Lisbon Cathedral then sit by the sea on the stairs on Avenida Ribeira das Naus, giving you a chance to people walk.
Head to the Feira da Ladra, full of knick knacks and vintage items. Walk to the Jardim do Príncipe Real to see the contrast from that area to Mouraria (below), the Principe Real part of the city straighter and narrower, with well-kept buildings. (If you have a chance to stop into the Museu Nacional de História Natural e da Ciência - Universidade de Lisboa it's not far! There is a fee though.)
For low-cost day trips, walking the areas of Sintra, Cascais, and National Sanctuary of Christ the King in Almada across the river are all accessible via public metro/train or boat and at very reasonable rates.
For a trip outside the city with a picnic basket in tow, try Parque das Nações, site of the Expo98.
Food! I can't not mention food :) The below are not expensive, and are delicious.
The market above, while a bit touristy, does have a great representation of foods from around the city -- it means you can share plates at tables with friends, trying roast chicken and porco preto (black Portuguese ham, fed acorns for most of its life, with a nutty, cured taste) all in the same place.
Head to the Martim Moniz square to eat in Mouraria -- in the middle of the square there are quite a few little pop up restaurants with cheap sangria and snacks. From there, you can walk up toward Cafe da garagem (med udsigten), located in the basement of a theatre with really great views of the city. Have a glass of vino and overlook the city before heading to dinner.
If you're looking for a place to eat lunch I would suggest Restaurante Zé da Mouraria -- portions are technically "For two" at about 12-15 Eur each, but they easily fed 3 or 4 as you can see below. Enormous. They are only open for lunch, though - not dinner.
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You can't miss the Museu Berardo, totally free and with great pieces of contemporary art. Most museums are also free on Sunday mornings.
Check out "Out Jazz Festival" with jazz concerts every sunday in different parks around the city.
Prices are considerably cheap for the US standards, you can have great meals in a typical restaurant for as little as $10.
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I live in Lisbon! There is plenty of things you can do for free here. When are you arriving? I would love to help you, and I can send you some personal city tours if you want :)
P.S.: I just returned from LA, I was there on vacations! Loooove it!
As many others here have pointed out, walking is the key answer to doing something for free in Lisbon. The views, the sense of location, the charm of a city as bewitching as Lisbon can only be obtained through walking its little back alleys and streets.
I wrote a short walking guide to the Santa Engrácia National Panthenon which may help get you started: http://www.unexpectedtraveller.com/Blog/santa-engracia/
Stroll around the city at late hours, listen to Fado, buy a bottle of wine for 2 Euro in a store and enjoy viewing the sunset overlooking the river.
With the summer here, kick it at the beach whenever you can. So many beaches to choose from, each with their own charm. Nothing more free than sun and waves and, well, a very cheap Sangria. Getting to the beaches is usually just a few euros.