My first time to Negril was an AI (in the 90s). We were told how unsafe Negril was. We were afraid to leave the compound.
After many, many trips (and a wedding in the cliffs!), Negril is safer than most large cities. Be smart - do not flash tons of cash or expensive "stuff" as is the case in ANY foreign area.
Be respectful to the locals - they are 99% helpful and hardworking (I actually the locals are nicer/more helpful than in many US cities!).
Get a real taste of Negril and get out of your AI. Have jerk chicken at a stand. Have a dinner in the cliffs. Do not simply go to Rick's tourist trap and think you have been to the cliffs (imagine going to Niagara Falls and thinking that was "seeing the US").
Have fun, be safe, and enjoy. With an open mind, it is impossible not to fall in love with Negril!