Glacier NP - start from the parkingtrailhead area at The Loop on Going-to-the-Sun Road (the longer option is to start from the Logan Pass Visitor Center trailhead) and head to the Granite Park Chalet, then up toward Swiftcurrent Pass and take the spur up to the fire lookout tower -- the view is pretty incredible.  I did a day-hike from The Loop to the lookout tower back in 1993 (on July 4th, no less), and it was both stunning and challenging.

Another summer option is in Grand Teton NP, and takes advantage of the aerial tram from the Jackson Hole Resort/Teton Village mostly used for winter skiing, but it runs in the summer to Rendevous Mountain.  Once there, take the trail down the west side of Rendevous Mountain and head to Marion Lake, then return down Granite Canyon to return to Teton Village.  If you're really into a longer-distance challenge, from Marion Lake you can take the Teton Crest Trail northward and return via Death Canyon (!).  However, if you happen to be there early in summer (June), there might still be some packed snow on parts of those trails.  One other bit of advice -- if you're wearing shorts, be sure to put sunscreen on the back of your legs, as descending on the Granite Canyon trail will put them in sunlight for hours and can result in very unpleasant sunburn (from personal experience in 1985).

Have fun!