Welcome to Rochester! I'd just like to throw out there that I do overnight, in-house/apartment pet sitting if you should ever need a sitter for a vacation/work trip, etc. My rate is $30 per night for the base fee for one pet. Add on an additional $5 per night per pet for each additional animal. (If you have like lots of cats, we can negotiate something else. Not trying to break anyone's bank). I have experience administering medications, if that's something your furry friend needs. I do work 8a-5p.m. and would not be able to let them out during the day. If interested, please send me a PM here, as I cannot leave my personal information on this forum.
I'm not sure what your price range is for housing, but I currently live at Timberland Heights on the NW side of Rochester and love it there. Maintenance has been super responsive to our requests, which is something I haven't had in a landlord before. For a 640 square foot 1 bed, 1 bath apartment, our rent is currently $860 per month, plus electricity (which is also our heat) and internet. All in all, our monthly housing/utility cost is about $1K / month. They do allow dogs, with a pet deposit and monthly pet rent. If you consider living there, please put me down for a referral: Sarah Kiehl 🙂
Otherwise, I have a friend who lives at SoRoc and enjoys it there, too! I believe they are animal friendly as well.