I have not been to Nantucket in over 15 years, but am eager to go back for the first time since having our baby last year. It will be just me and my husband (yippee!) and we'd like something super quiet and peaceful for 3 nights the end of June- we mainly want to eat, walk, bike to beaches and, importantly, sleep!
Please give specific recommendations for a quiet B & B or cottage. thank you!

You don't say what your budget is, but one possibility is the White Elephant, which is a hotel/cottage complex.

I haven't stayed there, but friends live across the street, so I have seen the "garden cottages," which looked nice. They're essentially studios but no kitchen. Some have fireplaces but don't know how much you'd use one at the end of June.
Pretty good location. You can walk to the beach or downtown, but it's away from the busiest areas.
Don't know the prices, but I'm guessing they're on the expensive side since everything on Ntckt in the expensive side.

thank you, i will check into it. we'd like to keep it $250 or less.

I don't think you are going to be able to rent a cottage for three nights except at a hotel with cottages, and White Elephant is certainly one option. I would also think a lot about the Sconset location of the Summer House (they have other locations). The Summer House has a fabulous restaurant, a pool, the beach is right there, and Sconset, if you remember, is charm personified, but there are now good buses to town so you don't need a car. I think they own the tiny picturesque cottages next door to the restaurant. $250 could be tough, but the end of June will be better than after July 1.
If I were staying in town, I might look at the Fair Street Bistro/Woodbox, an antique guesthouse of great charm (1712) a block from Main Street or the Ship's Inn, almost next door.

I live in Nantucket so I don't stay in inns, but these look nice from the outside, are well located, and I know the food at Fair Street Bistro is fabulous if pricy. Their neighborhood is a little quieter than Centre Street, where many of the B&B's are located.

I think the Summer House is a great idea for a quiet few days but it's nowhere near town.

I don't have any recommendations on where to stay on Nantucket because we usually just do day trips there. I did notice that TravelZoo is showing a special being offered at Harbor House Village though. TravelZoo .com -- type in Harbor House in the search box.

It's available for mid-week and has select weekends - 3 nights required through June 21st. $90 per night (promo code is Spring3). For only a 1 night stay it's $99 per night (promo code is Spring1).

Sorry, I couldn't get the link to work right when I posted it here so I just deleted it...

I stayed at the White Elephant this week and I had a cottage all to myself. Nice and quiet, but of course nobody was there yet If the rates are too high, you can check in with their sister place, Jared Coffin House. I stayed there last year and found it to be just fine. It was also a bit closer to town.

Centre Street Bistro was a wonderful and inexpensive option for lunch, check it out. If you like sushi, NoLa just opened up around the corner from the WE.