Aloha NoeCHZ,
Posting the question on the Oahu forum might get better answers since that's the island that Honolulu is on.
It's probably easier on your budget to find a room in a house somewhere instead of trying to rent an entire apartment. Can you get housing at the dormitory on campus? The other nice thing about room mates, other than less expensive, is that they can help you with finding out where things are and give you folks to introduce you to other folks.
Probably the least expensive method to live on Oahu is to find shared housing and use The Bus to get around with.
TheBus
Would you be able to see if the University has any shared housing lists available? There's usually some listed on Craig's List, but some (many) of those are scams so getting a list from the University would be better. Traffic is also extremely horrendous on Oahu, so try to live really close to the University.
If you'll be at the Manoa campus, there may be some rooms to let in the Kaimuki area, that's close to the campus and usually less expensive than the Manoa valley where the campus is located. Kaimuki is one valley over and accessible by a short road around the ridge between them.