Actually, there is a LOT to do on Oahu. Pearl Harbor can take almost the whole day if you spend time to visit the Missouri. If you are fortunate enough to be there when the flea market in the Aloha Bowl is on, that's your best bet for shopping - whether you're looking for cheap, fun stuff or nicer jewelry and crafts (think Hawaiian quilts), you'll find some of the best prices around there.
We love doing a circle tour of the island - and love spending time on the north shore. That alone can take a day (or two if you are real explorers - you will find all kinds of spots to pull over and go for a hike - once we had pulled over to review a map and watched a bunch of locals pull up, jump out of their cars, grab picnic baskets and head down a trail - we shrugged, parked the car, and followed to find the most SPECTACULAR waterfall we'd ever seen - had to be 75 feet tall - no signs, no markings - it was just there and we were the only non-Hawaiians back there aside from a National Geographic photographer, who took our pic and sent it to us later)
I would also recommend hiking diamond head if you have time, having dinner at Duke's Canoe Club on Waikiki Beach (very fun), spending a day at the Polynesian Cultural Center (Yes, it's designed for tourists, but we liked it), and taking a sunset sail off Waikiki - very romantic!
When it comes to traffic, Oahu itself isn't that bad - but driving in Honolulu is like driving in any other city - I'd stick to the city bus while in town unless you don't mind city traffic and like having the control to come and go when you want - most things are very accessible off the bus routes, it's convenient and inexpensive. Check some of the 'standard' guidebooks, ie Frommers for suggestions - or ask the hotel concierge. I'd say rent the car for outside of town and take the city bus or a cab for things in Honolulu.