Hi, cost of living really depends on how you want to live. If it is just you moving or you are moving as a couple you can get one bedroom apartments in nice areas, gated community varying between JA$45,000 to $60,000 furnished depending on the area.
Groceries are in my opinion fairly expensive in comparison to the UK (I can only compare to the UK, I have no other comparison) but for a couple weekly about JA$7,000, depending on how you shop. Naturally imports are expensive. Petrol is expensive more or less everywhere at the moment, I can't give you exact pricing. There are a lot of restaurants and bars in Kingston.