Pop.
I don't know which Dominican airport is closest to PAP (Port au Prince). As pointed out, some may be closer but may not be able to accommodate some types/sizes of aircraft for various reasons.
Being that I live on the Ocean in Playa Chiquita, north east of Sosua and the POP airport, we are able to see most of the incoming/outgoing planes. Though I don't run out and look at every one, the increase in air traffic was very noticeable. My neighbors and I had noticed a fairly good increase in planes a few days after the earthquake in Haiti.
Five C-130s (?) taking off are very noticeable being that they are low and throttled up (heavy) as they go over us heading east then turning south/inland and then heading west toward Haiti still slowly gaining altitude. A couple of medium sized jets painted gray have been seen as well as other non-commercial jets. Many smaller private/corp/charter planes have seen. Even a couple of Coast Guard ? helicopters racing by going west.
I don't know if they are coming into POP to refuel, waiting for a landing slot at PAP, unloading or going somewhere else.
We have been to POP several times in the last two weeks to pickup/drop off guests. The commercial flights that our guests have been on have been normal for POP. We did notice a couple of medium sized jets on the tarmac that where not commercial.
We have also noticed that this increase in activity has slowed down in the last few days.