NY runs the entire month of May, with large tracts of state land open to anyone with a valid license and turkey stamp.

CT is open through the last Saturday of May, and I believe most of the neighboring New England states (NH, VT, RI, MA) run through most of the month. However, state land hunting is somewhat restricted in the New England states, most have a lottery system.

Your best bet would be New York, you still have 2 1/2 weeks AND Sunday hunting is allowed...