How much hiking are you up for? That will determine the best areas to visit. I prefer the east side of the park. If you want to camp and avoid crowds, or at least really big crowds, Two Medicine Lake campground is a little out of the way, but close enough to the park. If hoteling it, the Glacier Park lodge in East Glacier is nice, but rustic. No elevators, etc. I would avoid staying in Browning at all costs. Glacier is a big park, you can enter at either side and drive the Going to the Sun Highway and end up on the other side. Plan on a few hours, at least 4 or so, depending on how many times you use the pullouts to go WOW!!! Staying in Many Glacier will put you right at the east entrance to the park. So, I guess the real question is what are you looking to do there? West Glacier is the touristy part, rafting, helicopter rides, civilization, etc.
bob