I think Bar B Barn would be perfect for you, great location,right on the beach, not far from Shamrock grocery store. It's a really nice hotel rather than a guesthouse and have all the essentials. It's not too pricy. Make sure you call the hotel rather than booking online. You'll be able to negotiate a good price. I've got a friend who traveled alone and paid $60-70US a night BBB has always gotten good reviews as far as I know, in particular from female solo travelers.

Website: http://www.barbbarn.com/

Address:
Norman Manley Boulevard
Negril P.O
Westmoreland
Jamaica

E-mail: bar-b-barn@cwjamaica.com
Telephone: (876)957-9619