I cant believe you didnt get one good answer out of 5 repsones......
Your pump is going to be noisy either way so the best thing you can is build a little box and place the pump inside the box and run the air hoses out. You can do a wooden box but your best bet would be to find some type of smaller metal/aluminum box and place the pump inside and youll only need to drill holes for the air to sucked up and the air hoses. Other then that just insulate it the best you can and hope for the best. I have an industrial side air pump and it feeds 8 air hoses with just the one pump. Its loud but i built a box and can barly hear it.
As for your neighbors, in you live in a apartment complex or town home it is prob best not to grow unless its only a plant or two. Buuuuut if you must do it then say you are very into marine biology and have several saltwater fish tanks throughout your home. These require filters, air pumps etc so that would explain the buzzing sound you hear from the pump.
Im guessing the water drip your talking about is water dripping off the net pot into the res from a drip system you have set-up? If so then the easiest fix is to raise the water level to just under the net (where you want it to be anyway) and that should stop the noise of the water breaking the surface, if not it will def tone it down. If your pump is pumping the excess water directly back into the res then all you have to do is run a pipe just above the water line so theres no noise when the water cycles.
I have my grow setup in my bedroom with a big air pump, lights, fans, etc and i sleep like a baby at night. I can promise that the people above or below you wont hear trickling water or a faint vibration from a air pump.