Some of the most fun things to do in Lisbon are using the various modes of transport, so get your travel tickets ready.
Firstly take the best tram ride in the city, the 28 up to near the Castelo de San Jorge then wander through the Alfama, these days getting on it can mean a long wait, try going to the terminus at Prazeres and getting on there, also watch your belongings. There are a couple of other routes not as popular but still fun to try. Also try the modern tram 15 to Belem
The newly extended metro is excellent, some stations are like galleries or museums with works of art, definitely worth checking out the stations with the best installations.
There are four elevadores, three are similar to funiculars, the most used is Elevador da Gloria from Ave Liberdad to Bairro Alta, essential to start a night out. The second one Elevador da Bica from the Bairro Alta down to the river front and the third hidden one, from the castle side of the Av Liberdad, Largo du Anunciado, Elevador do Lavra. As you wander back down to Rossio there are some great cheap local restaurants.
Lastly the best known is really more a lift, the Elevador San Justa, from the top there is a walkway to the Bairro Alta and a café on top of the lift tower if you don’t mind heights, the view is fantastic.
For the best value transport take the ferry from near Praca do Commercio or Cais do Sodre to Cacilhas, they run frequently. Have a drink and a snack or lunch in one of the many places, see Farol above. The ferry back is wonderful for the views. Other ferries go to Barreiro and other places which are slightly longer journeys.
Estufas Fria & Quente are under the Parque Eduardo V11 at the top of Av Liberdad, they are hidden gems of greenhouses, pools, flamingos, with tropical and cold gardens, great value
Other more obvious sites are the Castle, Alfama and the Saturday Flea Market atnearby Campo Santa Clara
Gulbenkian Museum is worth a visit if a bit difficult to find, a huge variety of exhibits and lovely setting. Make sure you know which bus to get, with all the hills it looks much easier to get to than it actually is
Belem and its various museums and monuments also has the famous cake shop Antiga Casas do Pastels in Rua de Belem, the tram 15 goes but gets very crowded, an alternative is the train from the Cais do Sodre much quicker, very frequent but you will need a new ticket even if you have a Carris travel pass.
Expo Site has a great new metro link, there is lots to see, including a huge aquarium and very futuristic buildings.
Museu da Agua has various locations, including one near Rato with exhibitions and a great view from the roof.
There are several new museums and galleries which have opened in the last few years, including the Museum of the Oriente at the Doca de Alcantara.