I get to NYC 3-4 times a year and always stay at Hilton properties as I'm a Diamond HiltonHonors member. None of the Hilton properties that I have stayed at - Hampton, Hilton Garden Inn, Doubletree, Homewood Sutes, etc, have ever charged a resort fee. I do see now that the NY Hilton Midtown has a 'resort fee."
Many hotels in Las Vegas now have the resort fee. I've always asked upon check in to have it waived as we won't be parking there since we don't have a car, won't go to the pool/fitness center, won't need internet access or be making any calls. The front desk has always removed it.
Hilton will honor a lower rate from another travel website - Expedia, Orbitz, etc. Just call the hotel directly, ask for the front desk, and they will honor it. Don't ask for reservations as most properties don't have in house reservations and you'll be transferred to a central reservations office - no where near your hotel. Always, always speak directly with the front desk.