Do hit the normal tourist spots, but don't waste much time there, i.e. Eiffel Tower, etc. If you like art and want to see the Lourve, wear very comfortable shoes, get there first thing in the morning and plan on spending the ENTIRE day there. You will still only see 1/5-1/3 of the museum even if you spend the day.
Moulin Rouge: It's worth spending some time in the area. There are cool bars around there, and internet cafe where you can also call anywhere in the world, and don't miss the Erotic Museum; it's worth the 7 Euro entry fee.
If you are just dying to see some Americans or want American food or want to see where the black people hang out in Paris, then go to BoJangles.
If you want to Party then hit the Bastille area. There is nightclub/disco/bar after bar in this area, some look like Rush street in Chicago. You can just hop from spot to spot.
The African and Indian/Arab parts of town are great places to go if you want deals on fabric and other interesting items.
Quick Tips:
Bring COMFORTABLE SHOES!!! Get a neck or waist pouch to carry money. Bring a backpack with a lock for keeping your camera, maps, books purchases in. Buy a tourist Metro pass. Bring about 100 Euro with you so when you get off the plane you have some cash. Then immediately try and get some cash out the ATM. You will find that larger places accept credit cards, but many shops don't. Cash is always King. Bring 2 Visa Check cards and/or Visa’s from 2 different banks. It’s important that they are Visa check cards because ATMs like in the US have different affiliations but if you have a Visa logo you will be able to get cash anywhere. I have not noticed ATM fees at all except the non-bank ATM fee charged by my bank. Make sure you protect them so they are not demagnetized. The ATM’s have the very best exchange rates because you are exchanging Bank to Bank with no middle man. Don't get Travelers Checks. No one likes to accept them and you will end up having to cash them in, that costs. Don’t bring US money and exchange it, it costs.
Best Way To Get Around:
Walking can be fun and you get to see Paris and find fun stores etc along the way. Paris is filthy and there is dog crap in the streets everywhere so when you are walking around be on the look out for trash etc. The metro is a quick and easy way to get around and when looking at guide books etc after the address the metro stop is listed, so if all else fails you can find anything via Metro. The Metro stops at 1:00-1:40AM or there about and starts back up around 5:30, keep this in mind and make sure you enter the metro by midnight so you can get to your destination. Also try some buses, if you take the Metro everywhere, you will miss seeing a lot of the city. Hopefully when you are in Paris there won’t be a strike like when we were there. Taxis are excellent. We had very good luck with Taxis. Write down the address of where you want to go and also the metro stop. A Cab ride at night never cost us more than 6 or 7 Euros.