There are a few polish delis in stamford. Warsaw deli off greenwich Ave has them

You're gonna have a hard time finding anything in your price range. Neighboring cities aren't much better either. Unless you want to live in Bridgeport. If you don't mind taking the train, I'd recommend looking somewhere on the metro north line. You'd probably have a better chance getting a place in westchester, or new haven county

It gets worse every year. When I moved to stamford 5 years ago, you were still able to find a one bedroom for less than 1500 dollars.

Good luck with bmr. I was on the bmr list for 2 years. Even knew someone who worked for leasing at harbor point. Couldn't help me