Mount the compressor on vibration pads. A really big one is dealing with intake noise. For my 20 gallon belt drive I dropped 8db by changing from basically an open air filter to an "automotive style" filter plus about 14" of rubber hose.
Take a look at this video.
Forget about his PVC stuff. The filter housing is the same type I switched to. I also used a rubber hose like he did. I didn't put anything after the hose.
Believe it or not, that rubber hose alone makes a big difference. I learned about this with a California Air Tools compressor. It came with a 5" dinky vinyl tube you were supposed to add to the intake housing. I thought it was a total joke... until I tried it. It really helps for almost no money.
Still, others like adding a muffler after the rubber hose.
Basically, you can go for some type of isolation room but I would start by working on the intake. Just something to cut down on that intake chuffing helps a lot.