Honolulu is very urban, you hill have to go to the western or northern sides of the island to find some solitude... Kailua Beach Park (NE of HNL) is probably the closest. City buses can take you nearby, and I've seen turtles swimming there. There are two miles of quiet sandy beaches east of the park.

That island, Oahu, actually has the best choice of beaches of any island in Hawaii. I have been to all the islands and now prefer Oahu for that very reason. The key is to get out of Honolulu to either the Windward side or to the North Shore. Beautiful beaches in both areas. The Windward side has two beaches which are consistantly voted as the best beaches in the USA: Kailua Beach and Lanikai Beach. Kailua beach is a long arched beach which often has kitesurfers, has no hotels or high rise buildings. Its a comfortable non tourist beach. Lanakai beach is smaller with very fine white sand, narrow in spots, and milder wave action due to sheltering reef. Two islands are just offshore making the setting unusually scenic. There are others as well including Makapu which has a terrific, more remote setting with interesting surf and currents. If you head up to the North Shore there are a number of excellent and storied surfer beaches Sunset, Pipeline, Sharks Cove (snorkel), three tables, and famed Waimea (nice set of jumping rocks/cliffs in the summer). Note: time of year makes all the difference in what to expect. Winter in the North has huge surf while summers have very calm and clear conditions. Windward seasons are the reverse, little surf in the winter but sometimes has the only surf on the island in the summer. There's decent public bus service if you don't have a car. Enjoy!

Maili Beach is also kind of out of the way but has very rough waves. (I almost drowned there.) This is were Puka-Shells where gathered when they were extremely popular. http://www.hawaiiweb.com/oahu/beaches/maili_beach_park.htm