Well, Moss Mountain Inn is beautiful and you will love it there! That said, most of the spectacular hiking is on the east side of the park or off the Going to the Sun Road. While at Moss, hike the Trail of the Cedars and also up to Avalanche Lake (same trail). Parking lot gets full early so go early morning. Drive up to Logan Pass Visitor's Center (also another place where parkign is premium so get there early) and hike out to Hidden Lake Overlook, less than 3 miles RT. You could also hike some of the Highline Trail - just go out as far as you want to go, the scenery is pretty spectacular. A beautiful hike which starts at Siyeh Bend on the GTTS Road is to Preston Park, less than 7 miles RT. A spectacular waterfall hike to Virginia Falls and St. Mary Falls in the same hike are pretty popular.

Once you're at St. Mary Lodge, I would recommend hiking up to Iceberg Lake, which you could do with the ranger-led group. Rockwell Falls which starts from Swiftcurrent lodge parking lot is another great hike. The hike around Swiftcurrent Lake is more like a walk than a hike, but beautiful.

Here's a list of hikes sorted by difficulty if that helps to make your decision:
http://www.hikinginglacier.com/hiking-glacier-national-park.htm

You won't have a problem finding a grocery store in the Columbia Falls area, but once you're at St. Mary's and Many Glacier, plan to pay a lot for food supplies.

We ate at the Park Cafe in St. Mary when we were there last September. Nothing fancy, but the food was very good. I read recommendations for it on various travel forums.

Agree with wave725 about the Virginia Falls/St. Mary Falls hike. Beautiful.

You're going to a gorgeous area. Enjoy and safe travels.

Highline trail MAY open this weekend though it will be muddy and you WILL cross snow fields. Advise checking with Rangers at visitor's center for this trail.
Avalanche Lake and Logan pass is accesible by FREE shuttle bus. Both parking lots will normally fill by 9:30 am. Unless your an early riser, suggest you park at Transit Center and take advantage of the shuttle which travels the length of the GTTS road. Shuttles run 7am to 7pm

While you're on the western side of the park, you could take a day trip to the National Bison Range near Moiese. The drive there by Flathead Lake is scenic and it's fun driving the wildlife loop to see the bison and other wildlife. (We even had a herd of bison walk around our car while we were on the wildlife loop.) There are two places where you can get out of your car for short hikes which take you to spots overlooking the park. There is also a good visitor's center and picnic area.