act0fgod: It's a little sketchy getting to the Nimitz Bike Path from Ala Moana. I wouldn't ride on Ala Moana. There are some side streets to get around some of the mess, and it has a bike lane for parts of the trip. I would go up McCully to Young (or King, though, a two way bike lane on a one way street... hmmm head scratcher), through the City Hall, to S. Hotel st, where there are only buses and bikes allowed. Then after you get through Chinatown, there is a little sketchiness.
I have a route map on strava getting to Hickam, via some safer routes, though, ,there's a part where you're on Kamehameha for a short spell, have to take a lane to get to the start of the bike path. It's quite rough until you get to under the bridge. The sooner you can get off (I assume you have a military ID?? -- make a left on Elliott, right off the hwy), the better.
Most of my workout/rec rides take me east/towards Diamond Head, not (west/Ewa)