For lodging at that price and right on the Madison I would recommend Campfire Lodge and Resort. I have parked my camper there each time I have been there. They have a great Cafe' with good food.It is about 18 miles to the Park. Not far to the Gallatin. As was mentioned the Henry's Fork is about forty miles. The Ruby is just about an hour away.
The time of year late June is good if the water is down. The HF fishes the best in June or Sept. If you fly into Bozeman and rent a car your right on top of fishing.

There is a Spanish Rest. in West Yellowstone called Madriz, true Spanish food, not Mexican.

I prefer Sept and have been there for six weeks for the last four years. A great place for a father son trip.