Montmartre is wonderful, as many have suggested! I'd recommend trying to visit early in the morning to avoid the crowds, though, and to grab an early, simple breakfast at a café or boulangerie.
If it's your first time, definitely do all the touristy things, but also try to put aside some time to wander through one of the many beautifully manicured gardens this city has to offer. Jardin des Tuileries and Jardin du Luxembourg are two favourites! Tuileries is filled with beautiful statues and is right in between Place de la Concorde and the Louvre and is worth a stroll. Since Paris is super walkable, if you're okay with not having an itinerary that's set in stone, it's fine to simply wander and see where the streets take you! A sunset stroll along the Seine is a must, we get the best sunsets here. <3
If you have the time for a day trip, Versailles is always a safe bet. It's about 30-45 minutes out from the city, lavish, and totally worth the visit if you're a history buff [or are just into incredibly beautiful architecture and craftsmanship!] I'm biased though, since I live here.
Best of luck, and I hope I was some help!