mirage shakes
 

just bought an 01 mirage DE with 78k on it, it's a daily driver bone stock.
Car had a shake (at 60-70) and a pull when I bought it. Balanced tires, still shook. Rotate tires, still shook but now pull REAL bad. New tires and alignment, no pull but shake now at 70-80. Steering wheel does not shake. Wheel bearings, tie rods and ball joints are good. Struts seem good, car does not bounce when pushed down and takes bumps OK.
What do I check next?