I've never had a positive experience with an off-site parking lot at LGA. In recent months I've only flown Delta out of LGA and have used the short term lot next to the terminal for parking without any problems. It runs about $30 for 24 hours in the short-term lot. Which I think is only slightly more expensive than the economy long term parking. I think my car is far from being a pile of crap (as described by the OP) and have never had a problem with vandalism, etc.