Absolutely yes.
I would look for a second generation (NB) Miata. Mainly, because I think it is the best-looking made, until they released the RF this year. The NBs all have the larger 1.8 liter motor (later versions of the first-gen NA Miatas had 1.8s as options). They also had optional 6-speeds with slightly better ratios for autocross and trackdays. Both NAs and NBs had optional Torsen Limited-Slip diffs. If you find an NB with a 1.8 and 6-speed, it should have a limited-slip diff.
Here is Road and Track's NB Buyer's Guide that lays out most of it -
http://www.roadandtrack.com/car-cult...-buyers-guide/
Red flags - avoid heavily modified cars, period. There are a lot of beat up Miatas out there and if you're building a race car/track toy/something you don't mind fixing a beat up Miata is perfectly fine. But you want a driver car - just avoid things that have been heavily modified.
I'm partial to the '99 10th Anniversary NB Miatas myself, the color is gorgeous, with a color-matched top and interior, they came factory 1.8/6spd/Torsen/Bilstein shocks. They're out there and your price range should allow you to find a cherry, low-mileage one. Similarly you could look for some of the other limited-edition models (all conveniently called "Special Editions) which tend to be optioned better than base models.
http://jalopnik.com/your-guide-to-ev...-so-1675339097