Scores vary by team, region, and kid...what you can get from mymeetscores is the basic number of kids that have competed in certain levels from certain teams over the last few years. Not all scores/meets are listed there and the athletes "top all around" isn't really that - its a combo of many meets so only a basic idea....that being said an athlete that is always scoring 37 on mymeetscores at each level is probably very good and one that is always (through the levels) listed at 32.5....pretty average.
Visiting gyms is important, as is meeting with coaches, and having your kid do trial practices. Any decent coach will be fine with that, and if you are seriously worried you'll be "kicked out of the present gym" for looking into options, then I'd leave anyway!!! This is your kid, and your money....as long as you are polite and honest, they should treat you with respect.
In our area there are 4 options (within a 3 hour drive)....one with great preschool programs and very scary/poorly trained optional level athletes who take years to even score out of levels, much less succeed. That can be easily seen with one practice IF you have watched other teams and know what to look for - form, strength, consistancy....etc. You can also get a vibe from the way the coaching staff interacts with the kids. One gym is simply too tiny (only a couple optionals, no 10s in years, etc....). The other 2 both have experienced coaches with track records of getting kids to college scholarships, reasonable success at meets, etc. One is larger, with a bigger compulsory group and more older gymnasts, one smaller, more optionals at younger ages, no boys team (can be a positive or negative)....depends what your kid is striving for and socially where they fit. Both could get a kid to college level, both have track records of lots of 9-10s (for our area, lots being different here, of course). Both head coaches competed at the Elite level themselves, although there are no Elites here (one kid was offered it but quit instead...)
At the rec level - just find one that seems fun and start out - you can easily change then...