You do not want to park your car in Manhattan unless you want to spend $2000-2500 a month on rent and $500-600 on garages. The parking tax is annoying, but you can get an exemption from the 10% surcharge as a city resident.
Where to find a place in 3 weeks? Are you coming to the City to visit? Brooklyn is nice and is a simple subway ride to work. Upper east, upper west, the village, tribeca. You can't really go wrong anywhere. If you use a realtor, many of the fees are paid by the renter, and others are paid by the landlord. It depends on the realty company in most cases. Otherwise, get the NYTimes--you can probably check the sunday classifieds online. I'll ask around and see if I can find you a rental realtor--PM me your info if you are interested.
I know your work area well. Welcome to THE city !
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-'13 E93 M3 Cab, Interlagos Blue, Carbon Black leather, DCT, all options, and fun, endless fun!
-'13 X5 35i M-Sport, Carbon Black & Cinnamon, Dinan Stage 2! 
-'15 Toyota Sienna Limited Premium AWD, Silver & Grey, Nav & BluRay, and less lame than the 2011 it replaced
-'07 Mini Cab S, Laser Blue, 6sp, endless fun that ended (sold)
-'04 X5 4.4i, loaded, loved, modded and sold
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