I went to Tobago, Great island.
You can email local kite spot they will help you out. Radical Sports Tobago
You can pay to leave your gear at the shop which is nice.
Pigeont point is very nice, there is a big surf break way out but surfer usually go to other spot on the island, i pretty much stayed in pigeon point since I didn't really care for waves back then.
As far as hotel I would skip those resorts.
Karkwak is really nice.
For very cheap I once stayed on Golden Thisle (i literally showed up on island for weekend without booking a room lol)
I stayed in Enchanted Waters too, was nice as well.
Since I went to pigeon point every day I didn't rent a car but there are a lot of stuff to do beside kiting so depending how long you stay you can rent a car...
From Crown point I would walk or take a cab to pigeon point depending on wind