Off the top of my head, the Ford Falcon V8 Supercar is an absolute dream to drive. Stable as a rock and surprisingly tossable it is a heavy RWD sedan.
So long as you only drive it on smooth tracks, the Chaparral 2J drives like it is on rails, and is an absolute terror to cars with PP numbers considerably higher as a result. The 2D is the same way, but it trades speed for even more stability.
Oops. Just noticed you said street cars. In that case, the NSX-LM is a really smooth driving, friendly car to drive; with a really linear power delivery and a controllable chassis.
The two HPA cars, the Audi in particular, are also both easy to control and quite fast. The various turbo Mitsubishi GTO/3000GT are also quite unflappable no matter how much power you dump into them.