Hi there. You'll get loads of opinions about where to stay but if you like laid back coupled with activity, I would recommend AC. You can always go to CC for a day or two.
I to am a female that traveled solo to AC in May and will be going again in September solo. I felt totally safe.
I have met so many wonderful people and not once did I feel threatened.
I would recommend staying at Exotic Caye Beach Resort. That is where I hang my swimsuit so to speak when I'm there. You can find more information out at www.belizeisfun.com.
Their prices may be a bit high, but if you call them Don and Carol would work with you on a price that you may be able to work with. OR I rent a one bedroom condo from Tuki Tuki at the same resort. You can contact her at email@example.com. She rents out her condo when she is not there and has a very good price. The location is about 10 minutes from downtown, has a fresh water pool, Crazy Canucks Beach bar and a dive shop on site. You would love it.
If you want to know more just drop me an email at firstname.lastname@example.org. I'd be happy to share more with you.
Whichever island you choose to stay, you won't go wrong. AC and CC are both wonderful islands but I would say that AC has more of a nightlife and more restaurants and shops to choose from.
Take care and have fun!!!