As to the rez. I''ve been in /around Browning either traveling through getting gas, (even tented a night in town to see the annual pow wow) off and on for nearly 30 yrs. and unless you're looking for trouble I wouldn't worry about it too much.
Many Glacier Lodge is pretty cool and the views are amazing, lots of animal activity, but not cheap. Its farther away from the rest of the park( not as centralized for the east side as St. Mary's is) but has a lot to offer. You wouldn't be let down if you stayed there for most of the vacation.
