Tomb Raider/Indiana Jones
Exploring ancient, crumbling ruins, full of traps and danger. This could work well as a "push your luck" game, where it's harder to heal and you're more seeing how many treasures(beacons) you can acquire before you escape or perish.
Jurassic Park
Abandoned structures, broken cages, dense jungles, and forgotten roads. The beacons could be generators, radio towers, etc - a mechanic where you had to visit them in a certain order might be good here, where you get parts from an equipment shed, restore the power, radio for help, repair a vehicle, and so on.
Your encounters would be dinosaurs, of course, possibly ranked by size/deadliness. A pack of raptors would be equivalent to a T-Rex, stuff like that.