As others said, you will be fine. Although it is not uncommon to have a driver accompany you to dinner, I will say that basically all restaurants in Negril are safe for single women and children. You may opt to just have a driver drop you off and then pick you up when finished. That will save you a few bucks for having the driver wait for you and purchasing him a meal, if he wants.

On that note, I will recommend Michael's On-Time Taxi, who posts on this message board. Michael provides personal service and his rates are very fair.