We were there for three days at the beginning of October.
We stayed at Miss Molly's Inn, a historic b&b-type small inn (it's where Marguerite Henry stayed when she came to Chincoteague to research for her Misty books). Even though it's close to a tiki-bar-type place, we heard nothing when inside the inn.
We really liked Pico Taqueria and Sea Star Cafe (and the Island Creamery).
For seeing the ponies, our best experience was with a kayak tour. We were able to get very close to them, and it was so nice and quiet. Also saw many gorgeous birds. We used Assateague Explorer. We also did their boat ride, but that wasn't nearly the wildlife experience and we probably wouldn't do it again.