Like others have suggested, I would start with CCA events and go from there.
Are you a CCA member already? If not, becoming one should be your number 1 step. Once you do, you automatically become affiliated with a local chapter. Local chapters organize and run HPDE's (driving schools) and you can see what events they run and at which race tracks.
The CT Valley chapter, Patroon Chapter, New York chapter and New Jersey chapter are all in your neighborhood as an example. Of course you are not limited to the events run by these groups, but rather by how far you want to drive to get to a track, as various CCA chapters run events all over the US.
As far as I know, CCA HPDE events are usually in the $175-200 per day, which buys you 4-5 x 20-25min track sessions, depending on the event. That is plenty time for a stock driver and stock car. They usually also include classroom instruction (mandatory) and some of them do wet skidpad exercises which is an incredible tool to learn car control at low speed.
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