I don't know about any pen turners in the area, but if you want some wood, you might try Re-Use Hawaii at 200 Keawe St. in Kakaako - just a couple of blocks west of Ala Moana Blvd. They are open 7 days a week from 9-5. They also have a lot of used hardware in addition to various reclaimed wood.
There is also a Woodcraft store near Re-Use Hawaii, but their wood is really expensive. However, there might be some turners there or they might know of some.
Winkler used to have a walk-in store in that general vicinity as well with a nice variety of woods, but they have relocated since the beginning of the year and are now an on-line only store.
There is usually a vendor at the Aloha Stadium swap meet (Wed, Sat & Sun) that has Koa wood for sale at reasonable prices. They aren't always in the same location, so you just have to walk around and look for a box of wood near the entrance of their booth.