For those in the Northeast, check out
http://www.emraracing.org/ for info on their time trials program -- tracks inclue Pocono, Lime Rock, Nazareth & the Glen. Also check your nearest track for other track or club days besides QC. Nelson Ledges has, for example, a "Track Dayz" program that's reasonable & local Porche, 'Vette, BMWCCA, etc., chapters often will have a not-too-well advertised event here & there. Alternate names, Solo1, lapping day, track trials.
It's what got me started almost forty years agon, with 26 years USAf and two marriages intervening until about 4 years back. Ah, one of the joys of being single, can go racing again!
Be certain to check safety requirements! If you ain't got it, you don't run!! (SA helmets, in some cases roll bar, harness or not, driver suit or long sleeve? -- all vary from one to the next.
Go fast, Have Fun, Be Safe!