What island are you staying on? If Oahu, a lot of people rent out parts of their homes over in Kailua and Kaneohe. Some are legal, some not. But Kailua is the total opposite of Waikiki and resorts. There are actually no hotels. You can rent places that are in walking distance of the grocery and restaurants. The Bike Shop rents bikes on Oahu and has a shop right in Kailua. Kailua is also a very nice beach (it's where Obama stayed recently). And your close to famous Lanikai beach. And there are a couple kayak rental places right near the beach.

VRBO has a lot of listings for Kailua.
http://www.vrbo.com/vacation-rentals...st-oahu/kailua

Now, when you say you prefer one of the smaller islands, well, are you aware that Honolulu is on Oahu, which is one of the smaller islands? The Big Island (Hawaii island properly) is my favorite island. It is the biggest, but also the least densely populated. In Waikoloa, which is north of Kona you can rent a condo. But--you're not going to get that living like a local feeling you could get in Kailua.

Maui has some neat stuff but overall I find the island too crowded. Molokai and Lanai don't have a lot of people. And they also have almost nothing for stores and restaurants.

Some folks love Kauai, and I like it quite a bit too. I don't know much about biking over there, although there is considerable hiking.