Love block island! I grew up a few blocks from where the boat leaves Point Judith.
Definately bring your bikes, you can bike anywhere on the island. Being your helmet though! Streets can be really busy.
Matunuck Oyster Bar is amazing but it's on the mainland and not on Block Island. If you are looking for a meal after you get back to the mainland it is fantastic. Expect a long wait and they don't take reservations.
On block island the Oar is fun for drinks. They are known for their mud slides and have a good lawn with lawn games.
The National Hotel has a good restaurant and is close by to the ferry. Other good places to eat include Three Sisters for lunch. The Spring House has great food and great views. It can be a little on the pricier side but even if you just go for a drink on the porch it's great.
If you want to go to the beach I recommend mansion beach and I recommend staying away from Ballards unless you like a party scene.
Visit Mohegan Bluffs either for hiking down or just for the views. It's beautiful!!!
Have an amazing time and let me know if you need any other recs:)