Picking a gym is like picking an activity: You should pick the one you're actually going to use.
If you're just starting out in terms of going to a gym at all, then going on a "vibe" is just as good as any other rationale for picking a gym. See if the gyms on your short list offer trial memberships, or if you can buy a short-term membership to try them on for a bit. Go during the time you would normally go. See how the gym fits into your life. See if the gym is rendered virtually unusable during _your_ usage times (which may or may not coincide with _their_ peak usage times).
If you're a little more experienced and know specifically what you want and don't want, then you probably have your own answer to your own question
The last criteria I would suggest, given the background in your profile, would be if there's a trainer in one of the gyms (if you are planning or thinking of using one) who works exclusively in that gym that has more specialized knowledge to get you to where you want to be, given your background. Linking in with more a more "tailored" knowledge source would definitely be a tipping criteria.