Lived there for a month in feb 2020. This post will be long so don't try to do all of it in your trip but I just wanted to get it all down so I can refer to it in the future if it comes up.
Getting around is easy via trains, walking and Uber.
Sintra certainly is worth the trip if you have time. You can take a train up there and sign up for the 434 bus day pass. Here is a helpful guide
https://www.sintra-portugal.com/guides/sintra-bus-434.htmlAs for sites in Lisbon, make sure to have time to walk around the Biaxa area where the Arch is and the plaza area in front of it. Great to be there for sunset and go to one of the restaurants around there for dinner and people watching. The Museo de Cerveja has good beer selection and ok food. Baa do Peixe probably had the best food to offer on the plaza. The Lisboa Story center is a museum there that is cheap and interesting, not a must do though.
So many cool areas to walk around there, take the Elevator up to Bairro Alto where you will find some cool bars and restaurants. Also the Pasteis de Nata is a must try Portuguese pastry and in Bairro Alto you will find the best maker of them at Manteigaria.
Another must see area is Belem. There you have the Jernimos Monastery, Tower of Belem which is the highly pictured fort out in the water and the Padro dos Descobrimentos which is a giant monument to Portugese Maritime achievements. You have to get tickets to get into the Monastery which is separate form getting into the Church of Santa Maria. The church I think is free to get into and very beautiful, but the ticket to the monastery is like $20+ euros. However it is worth it completely as it is one of the most beautiful and unique monasteries in architecture and detail. Next to the Monastery on the west side is the Maritime Museum which I really enjoyed. Also across from that is the metro Art museum which was ok (I liked the Museu Nacional de Arte Antiga for art more, its about half way between Belem and Biaxa). You can get to this area by bus but we preferred just Ubering there.
Third must see area is Alfama. This is where we lived for the month and where you will see most of the narrow streets with street cars that you see in Lisbon post cards. It is the only real old part of Lisbon that did not get demolished and rebuilt from the 1700s earthquake and flood. You can get there and get around there via the street cars which have pick ups around the Praa Dom Pedro IV. The castle you see way up on the hill is The Castle of Sao George and is worth seeing if you have the time. Also near there is Miradouro da Graa which is a plaza/park area where you can oversee all of the center of Lisbon. Lots of great stuff to just walk around in see in the area.
If you like cultural stuff, it's fun to go to one of the Fado restaurants there in the evening to catch a dinner and show. Parreirinha de Alfama is usually touted as the best. It's a very intimate experience.
For food overall, I highly recommend making a trip to Time Out Market food court, there are many good options there and it's just a cool experience. My favorite food experiences in Lisbon were usually other country's cuisines. I just could never really get into Portuguese food. They LOVE bacalhau which is a dried cod fish from the Northern Atlantic ocean. They boil it usually to rehydrate it and it just is not appetizing to me. I tried it at several different fancy restaurants and even mom and pop ones. They also love grilled sardines (big ones) and I couldn't get into that either. Nor grilled Octopus. For that reason my favorite Portuguese restaurants were more about the atmosphere and views than the actual food. So we loved Sol Restaurante & Jardim when we could get a table on the balcony or the Lumi Rooftop bar or Chapito a Mesa or Carmo rooftop.
Specifically, if I had only 3 days, I would focus on Biaxa area and Alfama for a day, Belem area with museums and the Time Out Market for another and Sintra for a 3rd.
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