monthly parking -any deals on the UWS?

Define "practical".

And what part of the neighborhood is this in?

Also define "appreciated".

What kind of appreciation should we expect to receive for providing you with a practical suggestion?

Are there any websites that show lowest monthly price in a particular neighborhood?

There's spothero, along with a bunch of other ones. Just google parking and neighborhood.

The garages tend to jack up their prices after the initial period, figuring people will cough up rather than go through the hassle of getting a new tax exemption.

We park in one of the Lincoln Towers garages run by Icon. Our rate 3 years ago was $200. Now it's $350. Still low for the neighborhood, but every 6 months or so our bill goes up :-( You can call this Icon number 212 873 8220 and ask them to tell you what is the best rate they can give you in the neighborhood (they operate lots of UWS garages).

One of the QuikParks (68th?) by Riverside Blvd. has a sign saying they'll beat any local deal by $50.