Anyone from Rochester ny know where I can throw a birthday party for my baby girl and it wouldn’t…

Not sure what your capacity or budget is, but have you looked into reserving a lodge at one of the parks? Depending on the time of year (for weather), the shelters are cheaper. The shelters at Hamlin Beach were nice and close to playgrounds.

https://www.monroecounty.gov/mcparks/reserve

There's also a rec building or something in Greece that was around $50/day that I was once told about, but I'm having a heck of a time finding it.

Her birthday is in October and since this is Rochester I don’t know if it will be summer,spring, fall or winter by then lol

Well the lodges are enclosed buildings with heat and such, and a number of them are around $150, but it depends on capacity and date needed. The shelters vary in amenities, and usually don't have heat (except maybe a fireplace), but even walls may or may not be included lol.

She would love the club house we always take our boys to the one in Henrietta and also adventure landing in Greece

I heard those places are for bigger kids