suggestions of places to visit

Uaxactun has a surprisingly impressive Classic Maya ceramics museum and some nice ruins as well and you can get there through jungle by chicken bus.

Hotel Peten is pretty nice and has a pleasant wading pool in its lobby, but Hotel Santana is also friendly and has a real one.

If I did not have too much time, I would visit Tikal and Yaxhá, staying overnight in Flores. With a little more time I'd also go to Uaxactun and Ceibal.

I agree, Yaxha should be way up on a traveler's list of sight to see in Peten. The setting is truly exotic and the array of ruins from completely restored to partially to not at all restored makes the ruin aficionado's visit all the more interesting. You can hike or take a boat to the ruins. There's cocodrilos in some of the waters. Horseback riding. Lots of treks.