Hello everyone!
I'm getting married in August of this year sometime (date TBD, whenever a venue is available). It's a budget wedding; I don't expect to be able to spend more than $4000 or $5000 in total...which really limits what I can do. Especially last-minute.
Thankfully, my family has connections to good friends who are licensed caterers, wonderful musicians, officiators, and I have DIY decor, my hair/make-up/dress all covered myself.
What I don't have access to are venues--I live down in Florida and won't be up in Connecticut before the trip for the wedding. This severely limits my ability to scout out venues in person. My mom and sister are willing to look at some places once you all are out of the deep freeze (stay warm!), but I want to have a list of 5-10 places before I send them off anywhere. And no worries--I didn't rope them into this unwillingly, and yes--I trust their judgement.
Ideally, the place would be indoors (need AC--I don't want to kill anyone in the heat!) but with a possibility for a cute outdoor photo spot. I'm hoping they allow outside caterers as well, or offer very inexpensive catering options. It's a dry wedding so I don't need to concern myself with alcohol expenses or permits.
It doesn't need to be in Connecticut itself, but preferably CT, NY, or MA only.
Have any of you had experience with some places in these states? My google-fu reveals gorgeous but very pricey and likely already-booked venues along Long Island Sound.

I'm thinking community centers, maybe? Or perhaps even booking a small restaurant somewhere to have the reception in.
Thoughts and advice appreciated--I have attended a whopping total of 4 weddings in my lifetime, only one of which was as an adult. The rest were much too far out of my budget to use as a model, one even being a black-tie event.