I second the Musée d'Orsay recommendation.
Bear in mind that the Louvre is huge. You won't realistically see everything in one day, so it's advantageous to have an idea ahead of time which bits you are most keen to see.
Buy lunch and eat it in a park. It's a very Parisian thing to do, and their parks are lovely. Try out a kouign amann, those things are incredible.
If you anticipate a bit of traveling around/exploring, consider getting a Ticket Mobilis. It's a day pass, gives you unlimited metro travel. The metro service is good, and frequent.
Do not believe the nonsense people tell you about Parisians being rude. They are generous and friendly, especially if you make a bit of an effort with very basic French (greetings, please, thank you, stuff like that). The first time I was there, I was starting at a map feeling lost, and I very quickly had about four people trying to help me.
Bistros are pretty samey, so after you've been to one, you may well end up searching for something different.
If something else comes to mind, I'll drop another reply.