We didn't have a whole lot planned upon arriving in Honolulu, which, in my opinion, can be a very stress free way to travel if you have like-minded travel companions. William and Randy stayed in a hostel near Waikiki beach and my brother and I stayed in a hotel near the convention center.
We found the city to be pretty easy to walk, especially if you stay near the beach. The bus system was super easy to figure out (especially with a smartphone) and went everywhere we wanted to go (including the airport) for $2.50 roundtrip, making our rental car an unnecessary expense.
Everything in the city seems to cost twice as much as you'd expect it to on the mainland: from food to beers to coffee; so avoiding expenses was really helpful. Luckily, all of the activities we really enjoyed were pretty cheap ($10~$20 per person per half day). My favorites included surfing at Waikiki beach, snorkeling with tropical fishes and sea turtles in Hanauma bay, and riding bicycles around the outskirts of the city and around diamond head crater.
If I had had more time I would have loved to see more of the east coast and the north shore and maybe do some sea kayaking. It seems like you could easily spend a full week on this island, but at the same time I'm really excited to get away from the crowds and head to a less crowded island.
As far as food recommendations go, I can't offer much because we got most of our delicious seafood for free at fancy doctor banquets. I can tell you to look on yelp for a hole in the wall hawaiian joint that sells plate lunches, they're great value and delicious. I'll also warn you at these same places to avoid pork lau lau...
Also, be sure to check out my report on the Kalalau Trail in Kauai, incase you decide to spend some time there. You could easily spend a week on any of the islands and not run out of stuf to do.
A complete photo album can be seen on Picasa. enjoy!