Work as a guide in Utah, here ya go:
What above said- Upper you wont be able to fish now unless you want to play with law enforcement at some point or a crazy land owner.
Middle section flows thru Heber/Midway. Great fishing but can be crowded depending on day and spot you choose. Lots of access points, you will see Provo river restoration signs. Pull onto dirt roads, park, walk, scope it out. Water levels are low, easy to get around right now, find deep pools, try diff. flys.
Try diff. nymphs, I like sow bugs alot. sculp zilla, dark purple wooly bugger can work magic too.
I tend to use a single fly, diff. weights depending on water speed and depth once I figure out the right one. 50-60 inch setup I think with indicator. fly- few inches to 2.5 feet, leader-9 ft. something like that...
You could always try some ice-off fishing at a reservoir too. I was st Deer Creek yesterday, fished from shore, caught some big boys. Middle provo flows into Deer Creek. Also Jordanelee and East Canyon can be good.
Do: get license, pack it in and pack yo shit out
Dont: get skunked! hahahahaha.
you should be able to catch some smaller browns- good luck, have fun on your trip!