The Grove St PATH station is 0.6 miles from Liberty Harbor RV Park and is a quick walk even if you aren't in great shape. Using Google Maps, it says that it is a 12 minute walk, but I don't really remember it taking that long. It was less than 10 minutes for us with 2 kids between 5-8 years old. We were in our 50s and DH has had back problems for years.
The water taxi over to Wall St runs ONLY Monday - Friday during work hours and is $8/per person ($7.50 for sr) and that is one way. That was just a bit too steep for us, so we walked the .6 miles.
While we were there, we saw several people getting taxis to go to the station. I have no idea how much that was, but figured it was too expensive for us.
If you are wanting to be close to all that the NYC has to offer and don't care to have a "camping" experience, Liberty Harbor is the place for you to spend a few nights.