Accompong is correct...you'll have to go to Montego Bay (the closest to Negril) or Kingston to extend your stay another 90 days.
If you are planning on living here and you've no connection to Jamaica via marriage or family, you will need to apply for Permanent Residency, a Work Permit if you're planning on working in Jamaica or you could eventually apply for citizenship.
You haven't said if you've been to Jamaica before or if you're a regular visitor here but either way, you are going to need to spend more than a couple of weeks to "see the place". There's a lot to learn and understand and you won't be able to do that in a such a short time. Jamaica can be a fabulous place to relocate but even people that have lived here full time for years, have had issues with adjusting to the differences in lifestyle.