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There are rallycrosses near the Albany NY area, as well as the rest of new england. http://www.cny-scca.com/index.php?module=PostWrap&page=content/rally/2010RallyxSchedule.htm
http://www.ner.org/forums/index.php?board=3.0
We also have paved hillclimbs in Vermont hillclimb.org
I never thought about the Albany area.
But seriously, the Rallycross contact guy's name is James Quattro?
fitting isn't it....though I don't think he is in to audi's.
Another good one is manager at Vermont sports car, his name is Clint Fast.
10 times better name than say....Dick Trickle.
Its easy... If your prefer OMG Driiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiift go with the miata
If your prefer OMG BOOOOOOOOOOOST go with the wrx
if you want both, put a turbo on the miata 
Capt Slow wrote:if you want both, put a turbo on the miata
I'm pretty happy with this answer.
This is a tough one. If it's going to be a track day-only toy, I'd definitely go with the Miata. Like others have said, consumables are much cheaper, and they are pretty damn near close to being set up perfect in stock form.
If you plan on driving it elsewhere than just the track, WRX all the way. They are bigger, boost is wonderful, they are forgiving, and upgrades are still relatively cheap.
And this "glass tranny" talk is absolute BS. I abused the hell out of my old 2002 WRX for years, and I NEVER had a single problem. Much of the time I had it, the car had about 60hp more than stock as well. The key is not to drive like an absolute idiot. In ANY awd car, you're gonna encounter something breaking if you dump the clutch at 6,000 rpm like the Turbo Honda guys do. The WRX's weakest link is the transmission gears. Also, early ones do have finicky trannies, but using the right fluids, upgrading the shifter/bushings/etc. and not driving like an idiot will ensure that it will withstand years of hard abuse. 
All that said, if you go with the WRX, splurge and get the 2006-07. They have the better 4pot/2pot brakes, the 2.5L motor, a better gearset in the tranny, and 06's even have aluminum front control arms. Look for the cheaper TR (tuner ready or track ready) model, they are lighter too. You're gonna want that stuff, trust me. 
There's a reason Spec Miata is so popular. The Miata, properly equipped, is a blast to drive on the track. Everything that makes it such a great street and autocross car applies to the track as well. They're insanely reliable, even when driven like an absolute madman, as long as you attend to the basic maintenance. Two down sides for the Miata for me:
Power. Specifically, lack thereof. You've experienced it yourself - you'll outdrive the Subies in the twisties, but they'll outpower you when things open up a bit. Of course, adding a turbo or supercharger to your Miata would fix that problem.
Height. I'm 6' tall, and in my previous Miata I was always struggling with helmet vs. roll bar clearance issues. Even with a serious "foamectomy" on the driver's seat, I still had trouble getting myself sitting low enough. Eventually I took to running on the track with the top up, mainly to avoid being black flagged for it.
I've never driven a WRX on the track, though I've driven a few at autocross schools and ridden in one on a go-kart track. Great cars - I'd love to have one. It'll never handle as well as a Miata, but on the straights you can outrun a Miata all day. And they're much more sure footed in wet, or even cold track conditions. I spent a late March SCDA event at Lime Rock Bob Costasfooting around the track, just trying to keep the back wheels from overtaking the front. I was usually successful. Not always. That would've been a day for the WRX.
It's a tough choice. Both are great cars. Would you rather have a power disadvantage but awesome handling? Or a handling and weight disadvantage but awesome power and grip?
I'm glad I'm not the one who has to choose. 
There's nothing quite like almost smashing in the tailpipe on a Ferrari Challenge car in turn 1 at Sebring, in an almost stock (seat belt tower brace, YKS Radials on 14" Daisy's, had all the carpet removed for future SM build) 1990 Miata w/ 195k on the odo. 
