Kingston is safe enough if you know someone who can show you around. Being a reggae DJ, I've got a lot of contacts over there and when I go with the missus shortly after yourself, in winter 2017, I'll be going to some recording studios there to get what they call "specials" or "dubplates", which is where a singer or rapper cuts a track with your own name in it bigging you up.
The Rae Town district of Kingston has an oldies music night every Sunday night from about 9pm until the sun comes up again and many UK, US and European visitors attend that. It's just some bloke who sets his DJ stuff up outside a bar and people dance in the street.
If you spend the entire holiday in the Sandals resort, you won't see the real Jamaica.