Hi,
I've been there twice recently.
If you're wanting to dive out of Honiara it's quite good, there's Bonegi 1, 2 & 3 all within 15 - 30 mins drive.
All are shore dives that can feature reefs, wrecks (incl. penetration) abundant marine life and it's possible to hit 60 +/- metres if desired.
Aside from that there's the USS John Penn accessible via charter or further afield there's a B-17 and a Japanese Sub to dive on.
Check out
this link for a list of all the dive sites, it's mostly up to date.
Going as a single white female should pose no problems as long as your sensible. There are many that live and work in Honiara.
Of course if you're looking to hit the town avoid the dodgy clubs, recommendations would be The Captain's Bar, or Club Extreme or any of the hotel bars anywhere else you'd be advised to go with someone that lives locally.
Daily eating everyone goes to The Lime Lounge and the food is genuinely good even if it does take forever to get to you.
I thoroughly recommend using
Tulagi Dive as your dive shop, Neil is the best in the business and despite the name he is now located in Honiara. His local staff are first rate and his two instructors are second to none ( though they are good friends of mine so maybe I'm biased).
Hope I've been of some help and if you'd like to know more, drop me an email. I'll send you some pics.
Dammit, I wanna go back now...