For non-skate, touristy (but worth it) stuff: Walk around / window shop in Le Marais (a super nice area), the two big skeleton rooms at the Museum of Natural History are amazing, go up and over Montmartre for a good view of the city (plus you'll pass the Moulin Rouge and stuff), the Pompidou Centre is pretty good for contemporary art, Deyrolle is a fucking crazy taxidermy shop (go upstairs), Shakespeare & Co is an English-language bookstore with a neat history, the Catacombs are nuts too if the queues aren't too long.
Don't forget open-top bus tours, corny as they are you'll see a lot of the city. Oh, and maybe keep in mind that the Louvre is pretty damn tedious but you kinda have to go at least once.