Kailua - The Shack for Sunday morning football - games start at 0700/0800. $1 (in 2000) Bloody Mary's and screwdrivers starting at 0600. Greasy breakfasts, followed by beer/lunch/wings for the 1100 "late games."
Best Waikiki parking - Ft DeRussy. When I was a junior enlisted (up to sergeant, if I recall), it was $2 to park all day.
Great posts from the others; I had many memorable (and many more non-memorable) nights at Murphy's, Irish Rose, and the mai tai bar at the Royal Hawaiian. Avoid Moose's - it is the E-Club Waikiki.
Running: The trails on the windward side of the Pali and on Tantalus are some of the best and most scenic I have ever been on.
Diving: Oahu is not the best in the world for diving, but locales are plentiful and convenient. Some of the better (and more popular) shore dives:
--Electric Beach (Ewa): Cooling tubes from power plant draw fish and coral, and sometimes a few white-tips
--Shark's Cove (North Shore): Plenty of caves, coral, and lobsters, but (surprisingly) no sharks.
--Blowhole (From Here to Eternity Beach): Nice wall dive
Sports: UH football is cheap and easy to get tix for, but forget about the game - go for the tailgaiting! UH Waihini volleyball is incredible - 11,000+ fans turn out regularly for volleyball.