check out www.wyomingflyfishing.com, the web site for North Platte Angler in Casper. Mark's fishing reports are pretty good and will give you a good start. I have not been up there in a while, but could tell you that this time of year the weeds are going to be pretty bad which can make nymphing difficult depending on where you are planning on fishing. If you fish just below Gray Reef the weeds should not be so bad and you should be able to nymph pretty easily. It's the usual stuff up there: midges, scuds, san juans and depending on if any hatches are coming off: caddis, PMDs, tricos; mainly small mayfly nymphs. If you are having trouble with the weeds go with streamers, they always work up there. It has been hot so the water is most likely warmer than usual, which will make the fish hold in faster, more oxygenated water. Fish the faster ripples and runs or pockets. Good Luck!
A guy i know just got back from there...he said the waters high---but clear...and he had the most luck with patterns that were red...san juan worms and midges...also "rock worms" (which im not familiar with) but i imagine is similiar to the san juan pattern....perhaps a size 16 or 14.