Places like Bondurant, Barber, etc are fantastic, naturally. Top notch. But for those on more of a budget you can get excellent on-track experience and classroom instruction over a two-day weekend by checking out the events sponsored by the various local car clubs in your area. Usually they are sponsored by clubs such as Porsche, BMW, Audi, Mini Cooper, Acura and the like. You drive your own cars at these events but you do not have to own these types of cars or belong to these clubs to participate. You will see all types of cars on the track. These typically cost under $300 a weekend- quite a bargain!
I have participated in these DE's (Driver Education) events for a few years and although the learning never stops for me, I now instruct novices for BMW, Porsche and Mini events.
Believe me, you'll be pushed to the edge and learn a lot, but it's all very safe. You'll get all the speed you feel comfortable with (these are held at various race tracks all over the country so it's serious) so check your egos at the door!