I've not flown in NY State, but the majority of US airfields won't charge for landing, handling, or daytime paring. Quite a lot will make a small charge for overnight parking.
Where do you park? By and large, where you're told by ATC - in most cases, it will be parking in front of your designated FBO. At bigger airfields, it's sensible to phone ahead and confirm with an FBO that they'll handle you.
If everywhere is telling you they'll charge, I can only assume that you're phoning some particularly large and expensive airports. Here in the UK I'd expect to pay around £10-£15 ($25-$25) to land and park for lunch, but not in most of the USA where airports are generally already financially supported by the local community.
G