Lots of conflicting stories on this, but I was at South Beach when some locals showed me where a bunker was supposedly located just offshore. You can barely see it- supposedly some kids drowned by it many years ago so the blew it up to prevent future accidents. All you can see is a bit of Re-bar sticking out of the water. Not sure why there would be a bunker under water but that’s what they told me.

We try and get there around 10:30am, and spend all day.

You can rent mopeds, but the busy roads are narrow and winding and there have been moped accidents on Martha's Vineyard, sad to say. I'd suggest taking a tour bus if you just want to go to the cliff lookout shops. You could always take public transportation back and forth via the VTA bus. Their schedules are on-line. If you want to make a day of it, many people rent a JEEP. I've always wanted to do that and I live here!

When bringing your own car to Aquinnah, you have two parking options based upon your needs. If you plan to stay at the Cliffs for a short visit to wander the handful of shops and grab a bite to eat along with catching the stunning views, there is limited free parking along the upper road that loops up to the sites. The Aquinnah shops and eateries are set along an ocean cliff on one side and a hillside on the other. You can park at the top of this hill for free. Aquinnah recently passed a Bring Your Own Bag bylaw to help stop ugly plastic bag litter, especially those that end up in the oceans, so be sure to bring or buy a souvenir bag for your purchases to help in the effort. Be sure not to miss the Aquinnah Cultural Center located a very short walk further down the road along the loop. Ask a local, they will help you find it. It offers wonderful history of the Wampanoag Tribe. Only the sit-in restaurant has toilets for customers. The public restrooms are located down the hill along a paved path. Or if need be, there is handicapped parking right beside the restrooms. If you plan to spend the day in Aquinnah at the beautiful beaches, visiting the shops, museum and eateries, there is a public parking lot that you reach via Moshup Trail. This is a road off the base of State Road and is easy to get to. This parking has a nominal fee ($15), but you will want to get their early so that you can get a parking spot. This parking location is a long walk up to the cliffs or a longer boardwalk to the beach. The parking lot is dirt for those in need of that information. Make sure that whatever you carry-in to the beach, you carry out. We love our pristine beaches and need your help keeping them clean. There are no trash bins on the beach. Also, you need to know, it is illegal to take the clay from the cliffs. If you don't bring your own car, you can always take a Tour Bus, VTA bus, taxi, rigorous bike ride, or biplane ride around Aquinnah also. Enjoy!

I did not see any dogs on the beach.

It's a great beach for kids and teens, but as the previous answer states, there is a bit of a walk to get there. The main beach area closest to the dune crossover is a great spot with relatively mellow surf which is good for body surfing and swimming, and at low tide the beach is wide, great for playing paddle ball or playing frisbee. Just be aware that if walk a couple of hundred yards to the right off the crossover (heading toward the lighthouse/point) it becomes a clothing-optional beach. You may not want your kids venturing down there, although many families do seem to enjoy doing a little sight-seeing there.

Staying at the Duck Inn in Aquinnah has the advantage that there is a path from the Inn to the beach and from there an easy walk to the Gay Head cliffs. You have the advantage of free parking for your car.(The only area in the Duck Inn that I found "musty" was the rooms on the lowest level.) The the scenic Menemsha harbor is worth investigating. The Menemsha Inn and Cottages would also be a good choice for accommodations and food very near Gay Head. When making reservations be aware that some restaurants in this area may still be "off season" in June. Looking for accommodations in West Tisbury would also be a good location. For the type of activity you group is proposing, I recommend being in the immediate area, staying where they can get free parking and have an included breakfast so you can get an early start to the day. I do not recommend staying in OakBluffs or Edgartown although these areas are not that out of the way if the group wants a change of pace.