Hi Drew,
Two years ago I used South Orange Disposal (which oddly enough is on Millburn Ave.) for a 20 yard "roll-off" dumpster. You pay a flat fee plus the weight which in my case added up to the amount of the deposit (I think I put two tons of kitchen demo into it).
973 762 3880. I liked that they had a local office that I could walk into in case I had a problem (which I did not).
PS: They will advise you to get enough 2x4s to put down that equal the length of the dumpster so that the heavy steel wheels don't crush your driveway.
Not sure of the volume you need to dump, but consider a Bagster.
gonna need a dumpster in my driveway ("purging"). Any recommendations?