I'm in Stony Brook, and I don't get LTE, but I go to Smithtown and I get it. However, I don't think AT&T has made it all the way out to the Hamptons just yet, I could be wrong.
The hamptons on the eastern end of Long Island is very tricky... Service cuts out all over the place... COVERAGE MAPS MEAN NOTHING... That's why I'm asking people who live there.... Get it??