We ditched the A/I after 2013. We have gone to Negril about 12 times since, we have tried a bunch of different variations from basically what my boss lady calls "Jamaican Camping" to what I call "A/I lite". Here are my recommendations for good places to stay on your first non A/I visit.
NEgril Treehouse- Includes breakfast and you can get a fridge in the basic room to store beer.
Travellers- You can include breakfast with a GROUPON on just purchase thru resort. Fridges are included in most rooms now, just make sure you are booking a superior room or above. The breakfast is the among the best we have found on the beach. Their deck is right on the water so the vibe is hard to beat.
How we do it, You can buy a bottle or two of liquor on arrival at the airport, I grab a bottle of Appleton Dark and maybe another depending on mood. We use Joe Cool to get to resort, I have him stop at one of the Chinese Markets on they way and we buy a case or two of beer. It usually costs about $24 USD for a case of beer, give or take a buck or two. We also grab some snacks, so essentially our room is stocked with beer, snacks, liquor and ginger beer. You can also buy some juices for mimosas, all this is done very cheaply.
The rooms at Negril Treehouse or Travellers and both on par with basic rooms at the A/I. This is the best way we have found to do it. If you stay at either of these properties you can either stay on property all day or leave, totally up to you. This is a great way to explore Negril and then ultimately decide how to tailor your own vacation!
Good luck!