Glacier

If you cannot enter the park then there isn't that much to do in the area. I'm a bit foggy on the tix, do they just apply to the main road going over the GTSR or to all entrances. There is quite a bit of hiking available on the other east gateways to the park.

The Road to the Sun is the main reason we go there. If it's not open, I go another time.

I wonder if the gate from Columbia Falls is still left open and unattended this year. It was last year and I was surprised you could drive in and out of the park without a pass...

According to the NPS web site for Glacier National Park, you need an entry permit between 6:00 am and 5:00opm. Get there are 5:00 am and eat breakfast until the sun gets high enough to enjoy the ride.
Last time me were there, the Logan Pass parking lot filled up at 8:30am. If you enter the park at 5:30am, you can stop at the pulloffs on the way to Logan Pass and get there by 7:30am. You should get a parking stop and be able to enjoy some short hikes and still have time to enjoy the road.

Bob has the good advice. Unless they've added personnel (doubtful) the gates are unmanned that early in the morning (same thing in the evening). "The early bird gets the worm." Just have plenty of coffee to wake yourselves up! :D

As far as being too early to drive the entire Sun road, although that is usually the highlight for most folks there are still plenty of nice vistas and hikes. You're likely to see a ton of critters besides. Take warm clothing, though.

And remember, just about all of that part of Montana is beautiful. If you like art museums, visit the C.M.Russell Museum in Great Falls.