Has anyone found a great cozy cottage on oahu away from the big city? I am looking for something with a kitchenette, not too far from the beach, on the east or north side of the island. Although anything away from honolulu will do.
Also, has anyone found a good source for renting a small convertible car while there? whats available, jeeps? thanks

I can't help you with a romantic cottage on Oahu - I know a few on Maui. But as for the car rental, you might want to try your luck on priceline.com.

Making our first trip to Hawaii (Oahu) this August, and wanted same kind of accomodations as you do. Have reserved what looks to be lovely North Shore oceanfront duplex cottage for about $100/night.....but of course won't know for sure how well I chose until we get there! Full kitchen, oceanfront lanai, even a pool on the grounds. Try these sites:

vacationspot.com (found mine here)
10kvacationrentals.com
teamrealestate.com
monetco.com

A tip: watch carefully taxes and cleaning fees - several possibilities I looked at turned out to be not-so-affordable when I added these in.....

Vacationspot.com also has links to vactionhosts.com I would go for Lanikai on the windward side only 20 minutes form Waikiki and Honolulu and you can always inquire about proximity to the beach.

In Waikiki the ilikai has very affordable ocean view condos to rent call the desk for the condo business that has their office in building. Insist on being in the Main building all have lanais. The annex is not as nice.

Car rentals Cheap tickets based in Honolulu $50 a day for a minivan 1-800-377-1000 also on the web. We were told to join AA for a great rate sorry don't have the details. If you are based in Waikiki you might want to rent by the day. Cabs are expensive so you need to decide how often you want to get outside. I know the Island well and would not be without a care. Parking at the Ilikai is not expensive but I think elsewhere in Waikik it is.