For renting bikes on Oahu check with Boca Hawaii
, they rent bikes, if they don't have anything for you then check with the Bike Shop Hawaii.
Not sure where you'll be staying, but assuming Waikiki, you can head east and then around the east end of the island up to the north shore. Stay on the coastal road and you'll pass a lot of beaches and a few bars. On Oahu you can put your bike on the bus and then get off and ride very easily.
If I were visiting, I'd head from Waikiki East to Kailua, stop at Kailua/Lanikai Beach and then ride back. THat's about 60 miles. Kailua is a nice town with some good eats/drinks.
The next day, I'd ride over Pali to the Kam Highway then head up towards the North Shore and hit some of the beaches up there, keep going all the way to the North Shore do a lap of Pineapple hill (great views from up there) then head back into Hawliewa and stop at Cholo's. Catch the bus back to where you started after a few too many margaritas.
On the big island I haven't ridden much besides the Queen K and up to Hawi, but a month ago we road the Queen K up to where you turn left to head to Hawi and we turned right. Followed the climbing road up to the town of Waikaloa and then back down, a bit more climbing, but a lot of fun too. Also, if you ride up to Hawi, keep going, go all the way to the end (gets a bit steeper at times), but there's a great view from out there. Stop in Hawi on the way up and then Kawaiiahe on the way back.
If you decide to do any riding on Maui, ride the West Maui Loop. It's a 55-60 mile loop around the west side of the island. Great views all the way (pretty darn hilly too).