I recommend Linston.........OK.....He's my son so I'm prejudged
Check him out at www.redplate-negril.com
He usually works at night and will stand by for you. The cost will be fair.
The going rate for a route taxi is 100 per leg and from beach to west end is two legs for two people is 400 each way. That is a public taxi so you will have to flag him down and may have to squeeze in with other passengers.
Linston will come get you and take you back for just a bit more. It's called a charter.
Capt. D