I use $130/month Bayridge Municipal garage on 86 street @ 5th Avenue
(BAYRIDGE, Brooklyn), cheap!. If too far from you, the reason I post is
because YOU can find another Municipal garage in your area by going to DOT
(dept of Transportation) website-->motorists-->parking, etc., find by
yourself. I hope you can find a real roofed garage, cause many others are
just open-sky parking lots and you dont need that.
Here's some facts about Bayridge Municipal garage I use

fficially open 8AM
and close 10PM, to get in/out other times you've to "bangle" on the metal
gate so attendat comes out and opens metal curtain, at other times you just
pass through by swiping your card out of car window, there's ALWASY space
and ROOFED/INDOORS, only the last (5th?) level has no roof, safe. Of course
no public garage is responsible for any damage, but again in a private
garage you can have a fire! This thing is concrete and steel, and fire
pumps everywhere, it's close to all emergency agencies, it;s a hot 5th
avenue/86 street area
IGNORE any notice you might see (in front) "cars left over 48 hours will be
towed" - management told us it's a leftover from old days when monthly pass
didn't exist (?) or was too cheap to justify overnight
attendants/security/nonpayments, people with monthly card and probably
others can stay as long as they're alive, I personally leave my NissanSentra
for sometimes over a week and I';ve seen a few CLASSIC CARS left for
MONTHS!! The same cars stay there forever, dont know why people dont drive
them....