I believe you can get half hour of free WiFi at Apgar visitor center. The rangers are great at providing recommendations of trails to do for your time and ability.
Entering at apgar/west glacier is a good place to start, lots of hikes around either side of lake McDonald (I always use the AllTrails app to find routes). Note that once you get into the park there is ZERO cell service and as far as I'm aware, no wifi. So expect to be cut off and to find a ride back out on a shuttle or hike until you're back in service.
It's a big place. Need to know what trails you might be hiking...BTW Hitch Hiking is legal in and around the park.
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