Vehicle size is restricted on the Going to the Sun Hwy:
Vehicles longer than 21 feet or wider than 8 feet (including mirrors) are prohibited on the steepest sections of the Going-to-the-Sun Road.
There are vintage tour buses that will take you over the highway if you aren't bringing a smaller vehicle with you.
The national park website has lots of information on the park and activities (http://www.nps.gov/glac/index.htm
Assuming you are arriving from the west side of the park, there are numerous commercial campgrounds as you approach the park. First come/first serve sites are available at the Apgar CG (which has sites large enough for your vehicle). I have stayed at the Glacier CG (outside the park) and Apgar CG and both were quite acceptable. The Trailer Life directory has a complete listing of campgrounds outside the park.
As far as activities go, there are lots of hiking opportunities in the park, ranging from easy to difficult. I would pick up a guide to the park at your local camping store so you can do a little planning for the trip.