In the park there are hiker-biker spots at St. Mary, Rising Sun, Avalanche, Sprague Creek and Apgar. Think they are all $5/person. Don't know about Two Medicine. Sprague Creek has maybe three tent pads for hiker/bikers. However, they are surrounded by a large, open (but shaded) area. I stayed there in '99 during a group tour and then again in '00 the same night as a group tour that I was not part of. There was also another couple there. There were so many of us that we were allowed to pitch tents on the grassy area. I have a hard time believing you would be turned away. In '09 we were there in late June so crowding wasn't an issue.
Two things I like about Sprague Creek are that it's small and it's an easy walk to Lake McDonald Lodge (IMO, a "must see"), which is a good place to grab a beer and sit lakeside. There is also a camp store at the lodge complex. However, the distance from Avalanche to the lodge is a non-issue if you are willing to use the shuttle service. There is also nice hiking at Avalanche. The major downside to Sprague Creek is that it's close to the road, so there is more noise many times of the day. Note that there are no showers at any of the campgrounds in the park except for Rising Sun, where there are some coin-op showers.
Outside at park at St. Mary there are a few private campgrounds. We stayed at the KOA in '99. They had a couple of group sites.
At Logan Pass, try to do the relaitvely short hike to the observation platform overlooking Hidden Lake. Amazing view, and you will likely walk passed goats.
If you do get shut out on the west side of the pass, I recommend this place:http://www.glaciercampground.com/index.htm
I stayed there before and after a backcountry hiking trip in the park. They only charge hiker/bikers $10 to pitch in the "meadow."
At the end of our '09 tour, we stayed at the Best Western south of the center of Whitefish on U.S. 93. Nice place with a hot tub that was more like a "warm tub."
Leaving the park, I recommend sticking to the ACA route. Not only is it nice back there, it avoids a section of U.S. 2 west of Hungry Horse that has no shoulder.
Bring plenty of sunblock. We got blasted by the sun on Marias. The stretch between Looking Glass Hill and St. Mary also has very little shade. But then you will enjoy a screaming descent into St. Mary. Think it's close to 6 miles. If I were riding your route, from Two Medicine I would try to make Rising Sun with a stop in St. Mary for lunch and any needed supplies. That would leave only about 2,000' of climbing to Logan Pass the next day. Get an early start and beat the crowds heading to the pass.
Finally, if you pay the entrance fee at Two Medicine, don't forget to save your receipt or you very well may have to pay again when you re-enter the park at St. Mary.
Have a great time!