As far as I know, there isn't much directly in Port Angeles. I have heard two different stories on whether there is a dive shop there -- apparently there was, but it wasn't considered a very good one, and it closed. Rumor has it a new one may have opened. There IS a dive shop in Port Townsend, and there is at least one very good dive site there, the Point Hudson jetty.
On the other hand, it isn't an insuperable drive from Port Angeles to Hood Canal, and there is quite a bit of diving available there, including several good shore diving sites and an EXCELLENT charter boat, the Pac Adventures operation.
The NWdiveclub site is a good resource, as is pnwscuba.com and Planyourdive.com
Hope some of this is helpful -- we really do have fantastic diving here, but rocky shores and strong currents can make some areas not very appealing for diving, and I believe this is the case around PA.