Well, you wouldn't want to keep it at your house, lest your family learn to recognize your -- I mean, that chick that looks kinda like you -- car. So, you'll want to buy another house across town, or at least a townhouse with a garage.
This raises another problem, however. Your own car will be parked at that other residence from which you emerge, driving the other car. We need another point of disconnect, or at the very least, anyone who sees you will suspect you are cheating on your wife with an ugly chick who kinda looks like you.
Thus, rent a hangar at your local airport, and one in a nearby town. Keep a third car at the hangar in the other town. You drive to your local airport, fly to the other, and drive THAT car to your second house, where you can glam up, and drive the
other other car out on the town. Reverse the process to return home. Please note, this method requires a pilot's license and an airplane. Fortunately, in this economy, houses and airplanes are cheap.
Oh, and to avoid arousing any suspicions, hire a crooked business attorney (redundant, I know) to set you up a couple of dummy corporations in which to hide those assets -- the house, the hangars, the plane, the extra cars. Some credit cards in the dummy corp's name to buy your avgas, a maid and landscaper who don't speak English but you pay very well to maintain the second house, and you're golden.
OR... if that's a bit much, you could join an extremely obscure sect of Islam that would require men to wear burkas 24/7. That way, you could be dressed as a man or a woman underneath, and no one would know the difference. Yep, your friends will say, "there goes Burka Boy again!" and your neighbors will report your now suspicious comings and goings to the KGB -- I mean, DHS -- but only you will know the secret. They might suspect you of a lot of things, but cross-dressing won't be one of them. Unless you live in a heavily Muslim neighborhood.
OR... you could fake your own death. Once your friends and family have mourned your passing for a sufficient period of time, and forgotten about you, you'll be free to do as you please -- start your life anew, so to speak. You'll have to change your male appearance somewhat to avoid being recognized from beyond the grave, but that's nothing a little hair dye and facial reconstructive surgery can't fix. A quick trip to your local flea market where your local illegal aliens obtain their fake Social Security cards will net you a whole new identity for a couple Benjamins. Bonus: since your new SS number belongs to Joe Blow in Ohio, you no longer have to pay taxes.
Well, there you have three options. Whichever you choose, I wish you the best of luck, sirrah, and may your closet always be cozy!