Definitely agreed with Hockey Ref that a campground reservation at Fish Creek the first night is a good idea. In July and early August, the major park campgrounds fill almost every night, and with a late afternoon arrival finding a spot without a reservation could be a challenge.
Beyond that, there are several different areas of the park you can visit, even with minimal hiking. The east and west sides of the park are very different geographically, and it's good to plan a little time in each. If you enjoy unpaved roads and getting away from the crowds, a drive into the North Fork Country can be very cool. Stop at the Mercantile in Polebridge for fresh baked goods, and then take the backroads up to Bowman and/or Kintla lakes. (Nice campgrounds at both those places, too.) This has become my favorite part of the park.
On the east side of the park, my favorite area is Two Medicine ... there's a good campground there, great scenery and short hikes, without the Many Glacier crowds. For a first visit, I'd recommend nights at both Many Glacier and Two Med.
A lot of the park's classic hikes are all-day affairs, but there are some really exceptional shorter ones, too. If you camp at Fish Creek, the short walk to Rocky Point is a good one, and heading up the Sun Road the two-mile hike to Avalanche Lake is a classic. Stopping at Logan Pass, the short hike to Hidden Lake Overlook has great views and a good chance of seeing mountain goats ... lots of people on that one, though. St. Mary Falls on the east side of the Going-to-the-Sun Road is great, and both the Many Glacier and Two Medicine areas have numerous possibilities for shorter, nearly-level walks to wilderness lakes and waterfalls. At both those places, the walks can be combined with boat rides.
There's all kinds of other information on this site, along with lots of hardcore Glacier folks ready to answer questions. Hope you have a great trip!
(Oh, and I have to say it: Glacier beats the heck out of Yellowstone!
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