Yeah. Try a rear sway bar first. You'll need an install kit since the 03+ don't have them, but the later cars still have the provisional holes to add one.
Order kit without bar or bushings here:
2001-2004 PT Cruiser OEM Rear Sway Bar Package $60
Then, pick whatever rear bar. Progress and Suspension Techniques make some of the thicker bars for the PT, and are usually the cheapest. About $140 shipped for the bar.
See what that does first. It'll not only make turning better, it'll firm up the rear suspension a little because it'll tie the left and right sides together, thus two springs and stuts will be acting more like one unit that without the sway bar.
The front sway bar is pretty big stock. In the 25 or 26mm range since I couldn't even tell a noticable difference visibly from the 27mm bar I bought for the front. So I'd leave the front alone unless it was an asthetics problem as the front bar is usually rusted.