Last summer, my girlfriend and I did a long road trip around the Northwest, down the coast, through the Grand Canyon and Arches. At Yellowstone, we came in the West entrance and explored as much as we could from our car. If you want a nice day hike at Yellowstone and don't mind being on a "crowded" trail, check out the hike up Mt. Washburn. There's a fire lookout up top with water. The views are spectacular.
To GNP, we took 90 to 93 since we were staying in the western part. We also took this route because we wanted to go by Flathead Lake. It's a nice drive and the lake is gorgeous. Plus, there are a number of small towns around the lake that sell all kinds of huckleberry products (although, I'm sure most smaller towns sell these to tourists).
A number of people recommended taking 15 up and cutting across on 2 to go through the Blackfeet Reservation. If you're staying on the east side and want to avoid Going to the Sun on your drive in, I'd suggest going that way.
Because our time was so limited, we ended up taking the full day red bus tour of Going to the Sun. At the very least, it was a good introduction to the park. We're already planning on getting back there to backpack. Site C112 at Fish Creek has a great view of the lake and is one of the closest to McDonald Lake.
For most of our trip, we stayed in NPs. We did stay in NFs from time to time to save money (most are free). I tried to avoid them when I could so the SO could have flush toilets and running sinks (trying to slowly ease her into the backcountry and didn’t want to shock her too much with NF sites).
I'm sure there are plenty of experienced Glacier people here to give advice on specific trails. If you're planning on staying in the backcountry in GNP, campsites fill very quickly. April 1-15 is advanced registration.