Your stay in East Hampton will be most enjoyable with a rental car, though you can easily uber any place you'd like to go. The only walkable area is Main St in East Hampton, and most hotels and Airbnbs in the area are not walking distance to town.
Assuming good vibes from Mother Nature, the beach is beautiful in October!! There is a beach right down the street from the Hedges Inn, so a great time to go would be before the welcome event Friday. To park at the beach, you need a parking pass. We have plenty at the Hedges Inn, so just let us know and we'll be sure you have a pass for any beach trip.