Water treatment options for on-grid gym facility

I'm working on a request for water treatment options for a small community gym that I'm part of. I've done some small scale water treatment projects in the past, but this has mostly involved off-grid systems. This gym is on-grid and receives city water, which tastes bad.

I would like to do an RO filter but I'm having trouble with the water hookups. In the gym, there is an industrial drinking fountain, and then a few sinks, that's it. The sinks are in the bathroom and one is in a janitor's closet.

Does anyone have any experience with hooking up an undersink RO unit (or other RO unit) to a drinking fountain? Should we get rid of the drinking fountain and install a water bottle filler tap instead?

We have a reverse osmosis system that we installed under the kitchen sink.

We did not do a whole house unit, though I believe there are those options.

Our system has a water spigot that we installed where the spray attachment was on the sink.

Does the gym only want the water fountain to taste better or the water fountain and the sinks?

For a drinking fountain, can the unit be installed underneath the drinking fountain or maybe on the other side of the wall?

Have you actually tested the water to know if the Reverse Osmosis system will work?
Have you tried just letting the water sit for an hour or so, in a jug?

I have access to the water quality data (I actually worked with the city on a separate project) and RO will definitely work and produce purer, better tasting, and healthier (if you're into that sort of thing) water. We're mostly only interested in treating drinking water. I think what I'll have to do is install the RO unit before the drinking fountain.