Have a wander around Marais - the gay district - plenty of decent bars cafs and nightlife (unless you're really uptight and paranoid of being around gay people, like many on GD).
Wander around Montmatre as it's nice and relaxed with windy cobbled streets (windy as in meandering, not sure on the micro-climate!).
Go up to Sacre Coeur - touristy but very impressive.
Beware of cafes in obvious tourist spots, you'll end up paying 10 Euros for a coffee.
Go for some drinks around Belleville in the evening - fairly happening area that my French friend took us to last time I was over there.
Get a strip of 10 metro tickets at the start of your metro travels to keep you going and so you don't have to worry about getting more every time. They're reasonably priced.
Visit Musee D'Orsay, wander around the foot of the Eiffel Tower (probably be a shame to waste your short time hanging around waiting to go up it), go see the Arc de Triomphe.
Paris seems to be a city that polarises opinion but I really like it. Have a great time!