I run mine right outside of the garage door with the garage door shut....no cover and the door dulls the sound pretty well.
My rule is that the power has to be out a minimum of 6 hours or so before I consider turning on the generator. Usually the storm is over and done with at that point (hence I don't worry about a cover).
At the 6 hour mark the power probably isn't going to come back on for some time (1-2 days) and so I use the generator to power the critical stuff (well pump, furnace, refrigerator). I fire it up to warm the house, cool the refrigerators/freezers, and fill the well pump tank, then I shut it back off again. If the storm was still raging, I'd probably bring the generator back in after running it. As I said, the generator usually doesn't get pulled out until post-storm.
Another tip....don't run high-amperage appliances at the same time you run things with solid-state electronics, including your furnace. High-amp appliances (say a well pump) kicking on will cause the voltage to spike, and will fry things that run on a circuit board. We'll run our well pump first, then turn everything else on.