I can count on one hand the number of times I've gone to Lisbon in my life (I live up north), and they were all just to see Sporting play. So I really don't know much about the city. :/
I guess I would say some of the places I would like to visit myself: the Belém Tower, Terreiro do Paço, the Santa Justa Elevator, the Pombaline Downtown, the Jerónimos Monastery, the São Jorge Castle... perhaps the ruins of the Carmo Convent too (destroyed in the 1755 earthquake, the ruins are still there) and I guess I would also go to the bakery where the original pastéis de belém (a delicious kind of egg tart pastry we have here) are made.
Aside from the more widely known stuff, not much I can tell you. :/