Name recognition across these three schools is pretty much equal in practical terms. No one who would have hired you coming from Skidmore would pass if you went to Bates or Kenyon, and Vice versas. Anyone recognizing the name of one recognizes the two others.
You seem to be an athlete, so your athletic experience is an important part of your overall college experience. It’s the last time you’ll play seriously at a potentially high level at a thing you presumably love.
It would be easier to give more color on the team dynamics if we knew what the sports were, but you said you’ve interacted with the teams so you have a sense. Your instincts for the teams are as good a determining factor as any. I don’t think your outcomes will differ greatly graduating from any of theses three. Opportunities to either be a star or play for a championship (or both) sound like they do, however.