Fun Holiday. Unless you are there at spring break, it shouldn't be loud, but quiet is not guaranteed anywhere in Negril...there's a noise ordinance that is somewhat erratically enforced but I don't think it applies before 11PM or 1AM.
Even in a quiet country area there can be dogs barking, roosters crowing, etc. In Negril you have that possibility as well as music possibly playing at nearby bars, nightclubs, etc.
Your best bet is a place with AC so you can turn that on and shut the windows.
If you are there in high season I can't think of many other options directly on the beach but in low a few more hotels fall into that price range. Low season is generally mid/late April through mid December.