I love reggae and Jamaican culture. When I grew up in Miami, we went on a bunch of cruises, and one went to Montego Bay, Jamaica. I've been to Jamaica a few times since then. It's only a 90 minute flight from Miami and isn't expensive if you are already in Florida.
Most tourists stay at expensive hotels or visit all-inclusive resorts like Sandals. Posh, but you don't see the real world.
Treasure Beach and Black River
Treasure Beach is in the southwest part of Jamaica. A string of coves with a small rasta population and a dozen or so guesthouses and hotels. I've spent as little as $30 a night, and as much as $100 a night for a room for two, no more than a minute walk from the beach.
There is one store, one sit down restaurant and miles of gorgeous beaches. You can be there a week and not see any other tourists. The tourists here are the independent travelers and backpackers. Just wake up, buy your $1 coconut breakfast, and walk around the beaches and village.
For transportation, I take local shared taxis for short rides. Shared taxis connect every city and village in Jamaica to one another. You only need a regular taxi for the long rides - like to and from the airport.
A short ride away is Black River. Black River is a small, poor Jamaican city. Not that poor, but you won't see cruise ship tourists walking around here.
Internet is expensive on islands, so I usually go in for an hour every few days. There are a few internet cafes in Black River. What's amazing to me about Black River is the authentic Jamaican experience. A real town, real stores and fast food restaurants and of course, a food market with fruits and veggies that you'll never see at home.
The experience in Jamaica is just walking around non-touristy areas.
Negril
But there are exceptions. Negril has a 7 mile beach that is a pleasure to walk back and forth. Touristy, so expect to be bothered a lot by Jamaicans selling stuff.
Oracabessa
Oracabessa is where Ian Fleming write most of the James Bond books, and his family owns a home and guesthouse here. I stayed in a huge house that a woman from NYC owned with her Jamaican husband. Two floors were for tourists, so we took a room there. A charming town - restaurants, a market, a quiet beach with only a handful of tourists and a good relaxed vibe.
Planning Your Jamaica Trip
Take a look at the usual travel sites, and pick a few towns and villages to spend 2-3 nights in each. Map it on Google Maps and you can just take shared or regular taxis in between destinations. Get out of the bubble of a 5 star hotel (but live it up!) and a regular taxi.
There aren't a lot of museums to visit, and most activities are "walking on a beach" or "walking through a town". You could do one day in each village and move on. In 10 days, you will cover a lot of ground.
If you eat at regular restaurants - sometimes good places and sometimes fast food, food costs won't be an issue.
For souvenirs, there isn't much to buy. I skipped the $30 Bob Marley CD's and got a few trinkets and kept some of the coins from stores. It's the beach vistas and experiences you will remember.