Back in my marathon days, I went for runs during layovers at FRA. Decent trail fairly accessible from airport. LH lounge to store bag and take shower afterward.

Interesting idea for airport fitness facility, but I think doomed by high rental rates air-side. And no one wants to deal with security re-screening for a land-side facility...which are usually available at airport hotels anyway.

There are a couple airports that do this, using local volunteers and expecting the visitor to pay all expenses. I think NRT and ICN are examples. There are also the big group tours organized by the airport, for example at SIN and ICN.