Bagan should be at the top of everyone's list. It is astounding. Take the balloon trip in Bagan if you can possibly afford it (it's not cheap at about $300). But it's a great view from up there.
I also liked Inle Lake quite a lot too. Beautiful scenery. Cool nights. Quiet.
Mandalay I didn't enjoy so much.
If you have the time making the trek to Sittwe and Mrauk U can be worthwhile. It isn't as amazing as Bagan, but has some nice places to see. And unlike Bagan the people still live in little villages very near to the monuments as they have for a loooong time. Tons of little kids running around, and lots of smoky cooking fires.
Definitely plan ahead. The tourism infrastructure is rather limited.