I get a pretty decent amount of shake in the steering wheel and can feel it pretty much all around once I get up over 65-70 mph on the highway. I just purchased about 2 months ago my '01 SSEi, has about 31K miles on it. Other than that, it'* been great so far! Any help or suggestions?

try and see if one of the weights on the wheel has fallen off, or you rotors are warped.

Rotors are warped, if it shakes braking at near any speed. Otherwise the wheels/tires could be off balance, among a host of uncommon suspension problems (which you probably wont have). Maybe a Balance/alignment would be a good idea.

has it snowed lately? The 2000+ H bodies are extremely touchy to wheel balance. If you get any snow in your rims it'* enough to cause that horrible vibration. I can bet once it warms up enough to melt the ice or snow in your wheels the vibration will go away. If it does it all the time regardless if it'* snowing or not, then your wheel balance is off. YOu have to make sure you get it balanced correctly though. Like I said, these cars are extremely touchy about their balancing.

No shake when breaking, so maybe I'll go the balance route. We have had a lot of snow, but the car is garaged every night, so all snow is melted off by morning when/if it does.

see if by rotating the tires changes anything, and have the tires rebalanced

First try a tire rotation. If the problem persists take it in for an alignment check. If that doesnt cure it there are a host of other things that can cause a shake.

'01 MA Bonneville, welcome where in Ma. are you? put it in your sig
as you can see Im in Quincy and work in Dorchester

I would say the tires. That is always what happens in my ride if the tires have issues.

It doesn't matter. I park in a garage too. Is it heated? If it is then it isn't what I'm thinking the problem is. If it isn't, then it still could be. Try taking it through a car wash and see if the vibration goes away afterward.