most clubs don't host TT. They have HPDE days where you drive on the track with a group. There is usually no timing but it makes for great practice. But you have to choose who you run with carefully. Most drivers that get kicked out of organized racing end up in these.
They are too many of them to list. The two I like are Speedventures or Redline Track events.
Here is a website that lists most organizations hosting track days.
http://track-days.org/page2.html