Did a day trip here last year (did not stay overnight).

You'll find (as I understand it) most all the shops, several lovely old inns, and several eateries located just steps away from where the ferry comes in, at the commercial center of the island.

Chances are you'll encounter minimum stay requirements here in high season. Note also that outside of taxis, there is no public transportation on the island. I'm not a bike rider, but my understanding is that this is a very good way to get around here. Had I stayed here, I'd have chosen a place in the commercial center area near the ferry landing.

Eli's is in this commercial center area and serves excellent food -- this is the place to eat if you value good quality fare. Open for dinner only, daily from 6 pm to 9 pm in high season. No reservations, so getting there early is a good idea, as reports suggest the place can get busy. Ballard's is a bar and restaurant on the beach and also right in this area -- food was okay, and it's probably as happening a place to hang out and have a drink as you'll find on Block Island. Open 11 am to midnight. Both the Beachhead (open 11:30 am to 9 pm) and G.R. Sharkey's (open 5 pm to 10 pm) are located a short ways north of the business district area and specialize in seafood -- had chowder at the former only, which was okay.

There aren't many tourist attractions here. The Block Island Historical Society Museum (close by the commercial center) is a dusty little local history museum and open short hours -- it's about like its less-distinguished counterparts on Cape Cod. Best I can tell, it's open high season daily from 11 am to 4 pm, but check first, as this info may not be reliable. The Southeast Lighthouse is a Victorian era brick structure and an attractive example of its kind, if a little expensive to go upstairs for the brief tour. It's located about 2 miles south of the commercial center, and there's a nice bluff view from its site. If memory serves, hours are a bit short here as well. There are other sites such as Settler's Rock (from all accounts, the local version of Plymouth Rock) -- I didn't see this, as it's at the northern end of the island and a hugely long walk away (and I didn't want to take a taxi to see a big rock, nor to see the North Lighthouse which is a further walk from the rock).

There are beaches here, but I didn't explore them much, as they're a good walk from the commercial center. Can't say what the swimming is like as a result.

Note also that like Martha's Vineyard and Nantucket, Block Island apparently has a very significant tick infestation problem. This for me precluded exploring things like the nature preserve Rodman's Hollow, located about a mile away from Southeast Lighthouse.

Here's one website with attraction descriptions:

http://www.frommers.com/destinations/blockisland/3172010029.html

The New London ferry arrives in New Harbor, a short taxi ride from Old Harbor, the commercial center described by bachslunch, where the Point Judith ferry lands.

My recent trips have all been short jaunts on private boats, so I'm afraid I can't really address the questions on accommodations and dining. Many, many years ago the Hotel Manisses part of the 1661 resort, had a good reputation for both. http://www.blockislandresorts.com/ Haven't been in decades so can't speak for it today!

Crescent Beach, near Old Harbor, often has calm waters. Block has some lovely vistas and great fishing (somehow I doubt that's your passion), but it doesn't have the sophistication of Nantucket and Martha's Vineyard. If you have good weather I think you'll enjoy a couple of days there.

Please, Please, Please do not let ticks stop you from going to MV or Nantucket or Block Island. Do they have problems with tick's? yes just like many places do! If you use common sense you will be fine, things like long pants, socks, long sleeve top etc. Better yet stay away from high grass and stay out of the woods and you will be just fine. And you can still enjoy all there is that is lovely about these islands. I go to Cape cod and Nantucket every year, never one tick on me. Common sense!!
Block Island was something I consider but changed my mind because there is not much there. I would look into a ferry to Martha's Vineyard or Nantucket for a weekend. It will be busy, keep that in mind.

Thinking back, it was the 1661 Inn, now a part of the eponymous resort, which had the better accommodations.

Thanks, everyone. Will follow on a few leads and return with questions. I've asked a few friends and most recommend spending only a night here, or even taking a daytrip, so I'll see..they also recommended going in early fall and not in summer, to avoid crowds.

The idea came about because Block is an easy jaunt from the North Fork, where I spend time in the summer. Would love to visit the Vineyard but that is a much longer proposition!

Block is a great place for a day trip. You can take the ferry, rent a bike and go all over the island. In the old days there were locals with cars with hand printed "TAXI" signs who would take you anywhere for a few dollars. We'd go out to the light house beach with our picnic and ask the guy to come and get us an hour before the ferry back. Someone would always show up at the appointed time. I don't know if they still do that, but in the age of cell phones you could always call a taxi to come get you.

ekscrunchy, Block Island on weekdays after Labor Day is perfect. No crowds and still warm enough to swim.

I spent about 4-5 days there some years ago - biking, hiking, swimming, snapping pictures. It was pure relaxation and if that's what you're looking for, it's definitely worth more than a day trip.

As others have said, most of the accommodations are within walking distance of the ferry.

I stayed at the Blue Dory Inn, a charming Victorian house just off Main St. It was lovely but it was a long time ago so I don't know what it's like now.

The passenger-only ferry I took to Block Island from New London arrived and left from Old Harbor (the commercial downtown):

https://www.goblockisland.com/default.aspx

There may be another ferry from here I don't know about.

Re ticks -- if one does proper preparation as Lmw_20 suggests, one should be able to avoid Lyme disease problems. But I do think it's important to mention this issue, as it may impact certain activities. Personally, I wasn't sufficiently motivated to do the precautions needed when I was there on my day trip visit -- I just did things that didn't require walking where I might encounter the critters, such as Rodman's Hollow.