Where you stay should depend on what you'd like to do.
There are many a/I's in Negril (as well as other destinations in Jamaica) that accept singles.
More info is needed to recommend a specific area or resort.
As far as safety is concerned, it's as safe as your home city. Don't walk alone on the beach at night etc.
There are plentiful cheap taxi's cruising the beach area, if you'd like to venture out to one of the restaurants or nightspots.