We stayed a couple nights at Mountain Meadow RV Park last July, right before the fire. It's on the West entrance side near Hungry Horse. We have a 16 foot Scamp and had full hookups, very close to a small shower house. Pretty nice.
check out two medicine campground near east glacier. last year we stayed last week may 1st week june. Wonderful. No problem getting campsite used heater only rarely. No showers here but a great place fantastic views and great hiking. keep this a secret ok.