We rented this lovely house for a week and found the space, amenities and neighborhood all very nice and convenient.
The house is clean and spacious feeling. The TVs are all very nice and there is a nice bonus room upstairs for kid games. The kitchen and bathroom supplies are very well stocked, and the backyard is lovely and pleasant to hang out or play in.
We haven't stayed in Bridgehamton before but found the location very convenient to Sag Harbor. We were a little disappointed with the restrictiveness of the south Hampton beaches but managed to find ones within a half hour or so most days. We went to Sagg Main beach during the week, Ponquogue on the weekend, and Montauk once since we were going to the lighthouse anyway.
Some places to enjoy: Nature Center was great, even for our 14 year old, Fresh Hamptons was pricey but had excellent food, and we enjoyed going over to Shelter Island one day for shell collecting and mini golf.
We also had very good/helpful interactions with the owner and their handyman when we needed a couple items.