I've been going to Negril solo for YEARS - always book your airfare and lodging separately. Contact the hotel directly for the best price - click on the links of the hotels here on Negril.com. Some suggestions for where to stay solo:
On the beach:
Negril Beach Club Condos
Bar-B-Barn
Yellow Bird
Fun Holiday

On the cliffs:
Samsara
Xtabi
Catcha Falling Star

No matter where you end up staying, you'll be fine solo - have fun!