Is this too "look good" or actually muffle the noise, because it won't do that well !
First, you want it as far from the house as practical. Behind a detached garage would be great, but the neighbors might not like it !
Second, I would build a wood shed and line it with 2-4" of foam board. You need about a 24" gap between the generator on the foam. You will need to mount about 1/8" steel plate about 2-4" off of the foam board (air gap) directly across where the exhaust exits the generator. You need to leave a gap of about 4-6" on the bottom to let air in. (The generator should sit on gravel or patio stones. This gap will discourage critter from trying to nest underneath because the don't like free air or light.) You also want to build this at least 8-10' high so that the noise is now very directional, straight up.
The best solution is to have hot air and noise exit out the top. An open top is perfect, but that does not keep the rain.snow out. If you are going to put louvered vents on the roof, you will need as many as you can get.