Plenty on Oahu to do for a week. Heck, plenty to do for a month for that matter.
Don't forget to visit the Iolani Palace if you haven't already. It's well worth it. There are guided tours or self-guided tours. You can even walk there from Waikiki so no car needed.
Regarding a hotel, I normally recommend
Waikiki Hawaii (HI) Condo Rentals | Vacation | Beach | Luxury
You can rent a privately owned city-view, fully remodeled condo for $99/night (plus a cleaning fee). Ocean view units start a little higher than that. But the building and the units are probably the best value in Waikiki in my opinion.
Downside is that they don't have many rooms at the $99 rate so availability is limited. Also, while I personally like the location (right next to Hilton Hawaiian Village) it is a little distance to the main strip of Waikiki shopping/stores.