What Ryan said. Also, mileage desired?
Generally, early July is the leading edge of prime backpacking season in both places. Permits should be workable for most any route. There should still be some snow in high places, but most routes will likely be passable without an axe. River crossings will be a concern (more a factor in Yellowstone). Bugs could be quite bad. Going-to-the-Sun road in Glacier should almost surely be open.
The classic northern circle in Glacier should be quite good that time of year. Highline Trail north, over Stoney Indian Pass, up to Elizabeth Lake, over either Red Gap Pass or through Ptarmigan Tunnel (which might not be open), then either Swiftcurrent or Siyeh Pass. The later could be extended south over Gunsight Pass, though that route might well call for an axe. None of the creek crossings should be especially problematic.
Yellowstone has a lot of pesky river crossings which will limit your options. E.g. I wouldn't want to cross the Bechler that time of year, nor the Yellowstone River south of Yellowstone Lake. A loop starting and ending at Old Faithful, around Shoshone Lake and with an out and back down to Three Forks on the Bechler, would be quite nice and have good variety.