I'm off to attend a wedding in NJ and will be spending a few days in NYC beforehand (July 4-7) and traveling with my 14yr old daughter. I have a hotel booked within a few blocks of Penn Station (30 E 30th St), but it's my back-up plan and costs a bit more than I like. I'd like to know what other people have done to cut costs and still enjoy NYC. For example, recommendations for particular hotels outside of Manhattan that are close to trains, places to eat, unique places to visit (other than the normal tourists things). Thanks!