Many great suggestions have been shared...I'd like to add/second some of them. We've been to Paris a few times, and used the Museum Pass well! Here are some of my thoughts:
Musee d'Orsay on the late night entry will give you more access to the art with less crowds. Also there is a cool model of the Opera Garnier, toward the back of the first floor galleries.
Same for the Louvre - we visited twice one heatwave day - about 5 hours in the day, and back again in the evening. It was a totally different experience in the evening - a good one!
Musee Jacquemart-Andre was a joy - I regret that we didn't have a treat in the lovely tearoom. If I get another chance to go I will be sure we did that.
Orangerie is beautiful, and I'd recommend getting there early for a more serene experience. They also have pretty Murano glass jewelry in their gift shop, which I loved.
Cluny Museum is small, easy to navigate, and filled with interesting things to see, from the tapestries to a narwhal horn, to heads from Notre Dame to beautiful stained glass...and a Roman frigidarium! This is in an interesting neighborhood to explore (Latin Quarter), and you're near the Pantheon as well.
Arc de Triomphe near sunset - the view of the city and the Eiffel Tower as the lights come on is really special
Tour of the Opera Garnier I think there was an option for a tour with entry - we did that, and it was great. Sitting in the rich red chairs, each with a name plaque on it, and looking up at the Chagall ceiling was memorable for me.
Fontainebleau was beautiful inside and out.
Sainte Chapelle on a sunny day - the stained glass was spectacular. You go in and then up to see the chapel. I didn't know that, and was a bit underwhelmed at first. But then...WOW! There are concerts there, too.
Not included in the pass, but interesting to do:
Musee Marmottan was a little tricky to find by combo of bus and walking - but it was memorable if you like Monet. Tucked in a neighborhood, it did not seem touristy there at all. A nice reprieve from crowds.
Giverny is worth a side trip if you can get there early in the day. We were the first group to get there on our tour, and the water was still (motionless) in the pond, reflecting everything beautifully. Monet's home is interesting, and the gardens were gorgeous. When the crowds descended, we were very ready to leave.
Lunch or snack on the rooftop cafe of either Printemps or Galeries Lafayette (I think I read that one was closed currently.) Great stained glass dome in Galeries Lafayette
Picnic in the Luxembourg Gardens by the Medici fountain (or really, anywhere)
Visit Poilane in the 6th, and consider a lunch of tartines at Cuisine de Bar at 8 Rue de Cherche-Midi or an ample breakfast of tartines, croissants, etc. Another location in the Marais - I've visited both. :-)
Jacques Genin in the Marais, an awesome chocolate, caramels, and pate des fruits boutique where there is a small and elegant tea room with a few choice items on the menu. I loved the award winning tarte citron. We met M. Genin while there - he was very gracious. We had tea, but I heard the hot chocolate was outstanding...so I'll get that next time.
Place des Vosges is another lovely place in the Marais to relax and watch people. The architecture is beautiful.
Have a great trip!
Laurie