We took a tram out the Belem part of town to see the Monument to the Discoveries and the Belem Tower. The transport network isn't the easiest to follow, so if you don't speak the language, try to find someone waiting at a bus/tram stop that does! Also, try to purchase your tram tickets in advance from one of the little booths. If you wait until you're on the tram, you will have to fight your way through a very crowded tram to get to the ticket machines only to find out that it requires the exact money. The part of town we visited was very picturesque. Because of this, I think people can get lulled into a false sense of security - there are a number of pickpockets operating in the area, and someone I spoke to had his wallet lifted at the tram stop. Although saying that, I doubt crime is any more rife here than at any tourist area.
This was a fairly quiet day for us. We climbed a big hill and played in a play park - that was about it! It's very pretty and there are a lot of touristy shops along the seafront and seafood restaurants on the road behind that.