A must-do day trip from Lisbon is a train trip to Sintra. It's just too close to not explore!
Because I love castles, I absolutely love Sintra. Take an hour train ride from Lisbon (Linha de Sintra) and then Bus 434 to avoid a 2-mile walk. The castles are clustered at the beginning of the Parque Natural de Sintra-Cascais. One of my all-time favorite sites is Pena Palace. You can't miss it becasue of its hilltop position and extreme coloring. It's a national monument, although it just from the 19th century. I won't explain too much more because there's a real joy in exploring it yourself.
Another castle that you must see is Castelo dos Mouros (Castle of the Moors). This castle is over 1,000 years old! Although it is mostly ruins, walls, and an occasional tower, it is great to walk in something so old. The views are spectacular, making it worth the stairs. Last but not least is the National Palace of Sintra. It is amazing that this palace survived from the middle ages and is really in great shape. The interior definitely outshines the exterior. I was most impressed by the large kitchen and the state rooms.