I'm partial to bars that offer a pool or beach or breeze or view or something, not usually into sitting in a hot bar by a road which means I skip a lot of probably great bars, at least during the daytime.
Travelers has a swim up pool bar as does Seastar, and Fun Holiday. I've visited all of these as a non-guest but with friends staying so am not sure about their walk-in-off-the-street policies (except Seastar, where it is fine).
I love 3 Dives though usually also eat there, not only drink. But I never ever walk by without stopping in.
Used to like to go to Tamboo and up to the top level and look at the beach passing by without the beach seeing me.
Alfred's dirty banana was the first drink I had the first time I stayed in Negril, still like to get one there occasionally.
MiYard...just about the only place for food and drinks at 4AM and the porch gets a nice breeze.