'Gator skins' are a brand of tire.
If the tires are starting to wear you'll get more flats, though this sounds more like a reoccuring problem, rather than new flats.
I'd remove the tire from the wheel altogether, and bend it backwards, so that portion of the tire is 'inside out' ... then run a cotton ball over the area. Anything poking through will snag the cotton and you should be able to find it.
As far as new tires go, if you're looking for something affordable, I've had really good luck with the Performance brand Kevlar belted tires. They're actually Forte, Performance's house brand, and they're about $12 each. Used the GT2/k and their cross tires.
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"There is no greater wonder than the way the face and character of a woman fit so perfectly in a man's mind, and stay there, and he could never tell you why. It just seems it was the thing he most wanted." Robert Louis Stevenson
