Good or bad room acoustics can be subjective. It is the ambience or "sound" that the room adds to the sound that comes out of your saxophone. The room sound can vary from a full on long reverberation that you would get in a large church, to a very short "ambience" that you get in your living room.
Sometimes it can be more of an echo, e.g. in a concert hall when much of the sound you hear is what bounces straight back off the wall behind the audience.
Furniture, curtains, people or acoustic treatment can lessen the ambience which you get more of when there are more smooth or shiny surfaces.
So good room acoustics are those that sound nice for the purpose. A reverberant church may sound good for a choir, but not for a rock band, as reverberation often sounds when there is a lot of bass. This is why in pop and rock recordings, it's often best to record in a studio that is quite dry (ie little room sound) and then add some room sound, the reverberation or echo in the mix where there s full control of how much and on what instruments.
If you record in a room that has significant ambience it can be a good thing if the room sounds good, but it is difficult or impossible to remove that sound from the recording, ie you are stuck with it. If a room is too reverberant for what you want, it can be deadened by hanging drapes, duvets or specially manufactured acoustic baffles.
More info here:
http://mediamusicforum.com/home-studio-acoustics.html