don't be hesitant about renting a car. the first time i tried it over 20 years ago i was too. but it was the best thing we ever did. once you get over the initial "freak out" period... which lasts about 10 or 15 minutes, you'll be fine. it's just driving. you do that all the time. it's really no big deal at all. as far as it being safe to leave your car... i've left rentals everywhere around the island. i've driven in all 14 parishes and never had a problem. sometimes someone will tell you that they were watching it for you and you owe them. just tell them that you didn't ask them to watch it and that it's a rental car and you don't care about it. (although you do.. they don't know that)
the only real advice i'd give you is this. definately rent the car. when driving between kingston and treasure beach the only area to avoid is spanish town and may pen. there is a by-pass around may pen so don't worry. everywhere else is cool. if you drive into the cockpits don't let people see you videoing without their permission. there is a lot of ganja in that area and they are kind of funny about cameras. so always ask permission. other than that, i've never had a problem anywhere.
do yourself a huge favor and drive. you'll be glad you did.