I agree with Freeagent12 above that Whitefish will be closer if you're going for a rental.

If you want to camp instead in the park, Fish Creek is my favorite campground, but I believe it's all full. It was tough finding spots when we looked a month ago.

So, hikes you need to do:

Avalanche Lake - This is a longish hike, but we've done it with young kids. It's an easy hike, and in the beautiful mossy shade of trees most of the way. It's an incredible payoff when you get to the lake. There are several waterfalls tumbling in that look like they're coming off the very top of the world.

Hidden Lake - This is right at the summit of the Going to the Sun Road. It's the hike that everybody does, but it's also amazingly cool. I have in front of me right now over our piano a photo my wife took of the view. On this hike you'll quite often see Bighorn sheep (by the parking lot), and almost always mountain goats up at the overlook. We usually take a lunch in our backpacks, and eat at the overlook. On this trail--true story--I was licked by a marmot. The thing came right up to me while my wife had the camera. It sniffed my boot laces first, then put it's front paws up on my shin, and started licking me. I have photographic evidence somewhere.

Many Glacier - Good ol' Turd above mentioned it, and he's right, it's a nice trip up there. We didn't hike much, so ask him for tips.

The West Side - Not many people go up the west side of Glacier because it's a dirt road. But it's a nice dirt road. We take our canoe, and hit one of the lakes up there for some fun, beautiful scenery. We also take a picnic, and usually eat on the shores of Kintla Lake.

Lake McDonald - after a long, hot day of hiking, we go for a dip in Lake McDonald. It's cold, but very refreshing. And don't be a wuss--my kids all did it.

There you go, my tips.