Congrats on the car and welcome! :D
If you have air suspension, you will see a switch right infront of the ECT power button on the gear shifter plate. See the pic below; excuse the 5th gear; this car is a '99, but the air suspension switch will be the same. Also, you must remember that the LS is no Porsche 911. This is a smooth, quiet touring machine with a roaring engine hidden under the hood. B) The car should feel controlled, but it will roll, so don't expect firm, linear reactions through the S turns. lol I suppose new shocks would help you if you do have the regular suspension since there's a chance that you are riding on the origional shocks. If you do have air sus. and you don't want it any more, you can put regular shocks in their place...many have done this mod to aviod air shocks that are $700+ a piece.
I hate to give to you the run around, but the 80mph vibration, could be a bunch of different things: lower ball joints, tire problems, drivetrain problems, mounts-engine or tranny, etc. However, if I had to pick one(after a tire rebalance), I'd go with the lower ball joints. ;)
Known LS problems are pretty much limited to leaky p/s pumps, front suspension componet failure(bushings, ball joints, etc.), and dead LCDs. Other than that, keep up with the tranny fluid and engine oil, and you'll be good forever!
See the detailing forum for all cosmetic issues.