This is a great question. And it does prove that everyone has different ideas about what makes a perfect gym..

And it certainly changes over time depending on your child's path in the sport.
I have a hard time articulating what makes a gym ideal to me. We've been at the same gym since the beginning for my daughter and I certainly know what I like and don't like about it. I don't believe that "perfect" exists and I guess as long as the good outweighs the bad (and as long as the bad doesn't include abuse)...
So the good at my daughter's gym is:
Convenient location and hours- it's about a 10-15 minute drive from school and from home. With practices every weekday starting at 3:30, I don't see how I would make it work otherwise. They have an evening group, even for the level 10s, and they start practice after school gets out. I'm so glad we don't have to choose between school and gymnastics.
Coaches that know my daughter and are invested in her - Honestly, there are times I don't really like my daughter's coaches. We aren't really friends and I don't try to be. Sometimes I complain about them. But at the end of the day, I trust them and I know that they are invested in her success and well being. Throughout her injuries and struggles, they have not given up on her nor pressured her to come back too soon. They listen to her and coach her in the way she responds to (which may not be the same way another gymnast needs to be coached).
A proven track record - Our gym knows what it takes to make it to D1 colleges. They are able to coach upper level gymnastics. This didn't matter to me when she was younger as much, but now I am glad that she isn't the only or first level 10 at her gym because I think all the others have made it easier for her and her peers to succeed. However, I am also glad that our coaches do not coach elite. I was never interested in that path for my daughter (luckily she wasn't either). I feel like it requires too much sacrifice (time, money, body). And I know a lot of gyms are successful at both, but I'm glad she is at a gym that doesn't train elite.
Atmosphere - My daughter has fun at practice. Not every day or every event, but she loves going. They play music and chat freely. They have contests and try and make practices more interesting by having different assignments and competitions. Most days she leaves practice tired but happy. I wish there was more team building activities outside of the gym, but that's not the gym's responsibility.
Things I don't like:
Communication - It's gotten a little better, but still isn't perfect. My biggest complaint here is when they decide to let practice out early or change the times of practice with hardly any notice. Nothing like getting a text from your daughter saying practice ends in 30 minutes.. when you are more than 30 minutes away or in the middle of something. So inconvenient! Also, now that my daughter is older, I really have no idea what she is working on or how she is doing day to day. We have meetings a couple of times a year, but I do think they rely on her telling me how things are going, when she usually doesn't.
There's probably more, but I've already written a book.
