Now we move onto the ice area:
Are the mats in good shape? If there are areas where its worn through (such as at the gates) are extra mats placed down? Are they secured in some way so they don't move around? Are there loose areas of mats where you could trip? Is there equipment lying around? Do the mats look clean? If they don't you'll want to take care to wear your skate guards.
Are safety rules obeyed? No one on the ice during ice grooming. Are the doors shut during grooming. One rink I went to had an announcement: "We are about to open the gates, please move slowly onto the ice." and the rink guards stood at the gates to monitor. Very professional. Do they keep people out of the hockey boxes during public? I don't like this rule personally, but I admit it's a good rule in general. Do you see hockey sticks or pucks on public ice? I've never seen this, but people I know have. Big no-no.
Are the rink guards clearly identified by a jacket or vest? Do they put out the cones? Do they actually patrol around the rink or do they fool around and mess with their friends? Yes, I've seen a girl in a rink guard jacket practicing jumps and spins in the center with her friends. Also hockey boys on duty playing with their hockey buds. Poor management oversight. On the other hand, I've been at a rink where the guards not only wear prominent orange blaze jackets, but red fanny packs marked First Aid and had Bluetooth headphones to talk to the front office (it was a huge facility). Nice touch. And they were clearly patrolling.
My observation is that rinks seem to vary widely on the competence of their on ice staff. Some are awful. Some are great. One of the best rink guards of all time was a teen age girl, weighing all of 110 lbs, who broke up a fight at my home rink between two hulking grown men.
The Ice: It's almost certainly going to be hockey ice. Why even bother hoping for figure skating ice. I think it's nice for the ice to be groomed at least once during a heavy public session, but locally this is rare. At one U.S. rink I was at, not only did they groom the ice mid session, they reversed the skating direction. I felt so Canadian. Is the ice deeply rutted? Does it have Lizard skin (aka tire tracks)? Condensation bumps? Toepick potholes? Thin ice? I had a home rink for many years that had a spot that occasionally showed sand. That was bad. Finally, is there a big pit like depression in front of the resurfacer doors? Does the ice tilt or undulate? Extra minus points for both tilting and undulating. There's something going on down beneath the ice to cause that.
It's probably not the dead rising from their graves causing the ice to undulate.
...Unless you're skating in hell.
Personally, I like rinks with high ceilings. I've skated occasionally at a local rink that had one of those lowered insulated ceilings. I felt like I was in a shipping container. But that's a personal preference. There's no safety, or business issue associated with it.
You'll note that I have completely bypassed the rink snack bar. You should too.
What's a deal breaker for me? Believe it or not, it's not the ice. No one has nice public ice anymore. My deal breaker is the booting up area. If I have to sit on the floor, it's not a good sign. The one rink where this happened, I now know to take a towel to clean up the floor so I can sit down. But the second thing is that at my age, seeing me get up from the floor in skates is like watching an arthritic cat trying to get up on the couch. It's a sight you don't want to see.