Hey, Glacier/Waterton and I go back for decades since I grew up close to that area. Beautiful, rugged scenery--and the best part, in my opinion, is it hasn't suffered the "gentrification" of so many wilderness areas. Tourist services in both parks veer more toward the quaint/rustic than high-style/luxury-wilderness establishments in the commonly visited parks. As a matter of fact, if you aren't enamoured of backcountry camping and prefer more modern $$$ accommodations, with wifi and better dining options, I'd suggest staying in the mountain ski towns of Kalispell or Whitefish just outside Glacier and going into the park for day hiking options.
If you prefer to hike and camp in the backcountry, though, you'll be in wilderness Nirvana. You've got some good suggestions above, but remember the park is huge so I'd second Rabbit's suggestion to plan where you want to go in advance.
Going to the Sun road is beautiful if you time it right to avoid the lineup of oversized rec vehicles and nervous drivers. I'd suggest going very early in the morning and stopping at the top of the continental divide to hike around for the day. Pack a picnic lunch and enjoy the views, then head down late day/early evening once the traffic dies down. There are a couple of nice day loops that we used to do when our kids were young and weren't up to overnight backpacking trips.
Another favourite hike was from the Canadian side--Waterton. From June until October both sides of the international park are connected by a small border crossing at Chief Mountain. It's a scenic drive and the border personnel are often quite chatty and friendly. Waterton is a very small, quaint park town that looks much the same as it did fifty years ago. There are camping facilities there as well as accommodations and eating places, and several good hikes that use the town as a trailhead. One of our favourite day hikes was to hike the Waterton Lakeside trail to the American end, Ghost Haunt and then return to Waterton by boat. The Lakeside hike takes about 4 hours, with a scenic spot to have a picnic lunch at the international boundary marker half-way down the lake. If you are up to it, you can do some interesting short loops from the American Ranger station at the Haunt before catching a return boat at 5pm. The boat ride back takes under an hour and is the perfect place to rest and take some more glorious scenery.
http://www.watertoncruise.com/index.php
The link also contains information about the Crypt Lake hike, another one of our favorites.
There is a good reason why Glacier/Waterton is on so many hikers' bucket list. I was lucky enough to spend decades hiking and exploring in the area and always found something new and breathtaking to see. You'll have a wonderful time!
