I agree with many others about Piper's Kilt in Eastchester: it's the gold standard for me, having grown up one town over.
The only other place that I would even mention in the same sentence is PLAN B in Simsbury, CT (northwest of Hartford). I think they have locations in West Hartford and Glastonbury as well. The burger is excellent quality, loosely packed, and juicy. Their buns are made for them by a local bakery I am told, and the parmesan fries are awesome.
This may even surpass Piper's Kilt for me now. Tough call.
I hear that the burger at Napa & Co in Stamford is excellent- that is going to be the next contender for the title.