$15/day seems to be pretty standard for the off-site places. I've used the Dollar lot (or maybe it was National?) and it was okay. I think the Crowne Plaza may be slightly cheaper, but it's a little less convenient as I don't think the shuttle runs quite as often.

Another option is on-street parking if you have the stomach for it. There are some areas not terribly far from LGA where you can leave a car for a week without getting a ticket. And there are some that are even closer where they only clean the street once a week. If you can find a spot where they clean the street only on Tuesdays or Wednesdays, that should work out beautifully for your schedule.