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I'd probably be an early/mid gym due to typing and theme.
Building is basically a giant museum filled with fossils and stuff. Off to one wing is the fossil reviver, the other side is a safari zone filled with fossil pokemon and rocks you can smash.
Down the center path is basically a jeep ride you can hop onto and are stopped at various points to do battle with trainers all of which have pokemon based off whatever is in the cage behind them. (Fossil pokes, Larvitars, etc)
My pokemon would be Tyrunt, Amaura, and Aerodactyl for the first round.
2nd battle later would be evolved fossil types, one from each gen: Aerodactyl, Tyrantrum, Armaldo, Bastiodon, Carracosta and a Tyranitar for good measure.
The whole point of the gym's research would be to discover the secrets of Fossil pokemon. And I'd be trying to unlock their true potential to figure out what their hidden typing was (aside from Rock) because not all ancient pokemon were rock type. So there would be attempts to find the mega stones that would restore the fossils to their original forms.