There are a few B&B and house rentals, but basically they are suburban bedroom communities that happen to be on the beach...although they would probably meet your needs for "sunbathing, swimming and relaxing".
You would need a car, and expect to drive to see any attractions, restaurants, shopping, etc...
Amaloo is correct. Kailua and Lanikai are not zoned for resort accommodations and there are no hotels. There are approximately 70 legal B&B's and vacation rentals in Kailua and Lanikai . Unfortunately, many of the rentals advertised on the web are illegal operations who do have the correct permits to operate. The majority of locals resent these illegal operations who have commercialized their residential neighborhoods. Currently the City has started to crack-down on the illegal operators and ultimately all of them will be shut-down. If you decide to stay in Kailua, be sure to confirm the B&B/vacation rental has a “non-conforming use” certificate to operate a B&B or vacation rental, otherwise you may not have accommodations to stay in when you arrive. Have a great trip to Oahu!
Just returned from 10 days in Kailua and it was wonderful. Kailua is 20 min. from downtown Honolulu, easy to reach, and wonderful beaches there & Kaneohe. Via rental car, easily visited beaches on the North Shore, all along the windward side of Oahu and tourist attractions such as Pearl Harbor, Diamond Head, Punch Bowl, downtown Honolulu, Waikiki Beach, Aloha Tower, etc. Saw Polynesian Village & luau, Hilton Village, International Market, etc., too. Found Waikiki extremely crowded and much more "touristy," with Kailua was less crowded and more private. Lots of sailboarding and para-sailing/surfing on Kailua. Mixed our days between driving to see attractions and just sunning on the beach! Our rental cottage was at the end of a private lane, just 4 cottages from the beach, an easy walk at any time and all beach gear provided! Highly recommend BEACHLANE2@aol.com! Prices reasonable and accomodations delightful. The town of Kailua has supermarkets, department stores and small unique boutiques, an open air farmer's market, theater and lots of surfboard, kayak rentals, etc. Also fast food and more local, delicious restaurants. Recommend highly as an "away from the madding crowd" vacation spot but close enough to give the best of both worlds.