Stayed at Fairfield in Livingston, MT last weekend. A brand new property about 1 hr (scenic) drive to Yellowstone north entrance - fairly convenient and the closest chain option to that side.

Close to freeway ramp but no noise, everything is new and in great shape. Rates are very reasonable now but i bet in summer you ll be looking at 200-300 range. We reserved an outdoor jacuzzi for an hour while it was minus 10F - nice way to relax after winter hiking/skiing in yellowstone and it was funny to see wet hair freeze into icicles within a minute. Breakfast handed out by staff - jimmy dean sandwiches to microwave and usual cold stuff.
Front desk folks were very helpful with room arrangements, 4 pm late checkout, and other stuff - they even proactively lowered the rate when we changed room type to get connecting rooms.

Got dinner takeout from Campione (also a new place 5 min away that opened last summer) and we all liked it so much that we ended up getting lunch from there next day as well. Very strongly recommend.