I find just upgrading your fans can make a huge difference. Those little pee wee processor fans are loud,Also Video card fans.. I hung a big 5" in there and now mine is very quiet. The bigger the fan they run slower therefore quieter.
I do sometimes put a small sound absorbing panel in front of the CPU which is under my desk.
Bottom line is the CPU noise floor is lower than that of my pre amps. :)
It would be a PITA to have the computer in another room.