DW and I can easily go a week with 80 gal fresh water doing dishes after each meal and showers every night. Dishes are done with minimum of fresh water, showers are pretty short (not quite submarine). I would make a BIG GUESS that 4 to 5 gal per person per day is a good (not being real careful of usage) estimate.
the bear II and darsben list really good water conservation ideas, using their methods I suspect you can get by with 1 to 2 gal per person per day.
Your black and gray are fine. Your fresh is probably gonna be dicy. Sometimes you can get a long enough hose to reach a common fresh water tap; sometimes borrowing and sharing hoses amongst other campers. There are some fresh water bladders you can mount on roof to transport water. You can get and fill a 50 gallon tank which can be pumped into your fresh water tank (you can do it with lots of 5 gal cans).
As enblethen said above, they seem to expect you to have fresh water, but no sewer; this is a pretty common setup at state/federal/county parks.
Your question was about water, but you did not mention battery capacity (so I'm assuming you are looking for sites with power). The vast majority of parks that have power have water at each site, those that don't usually have a lot of spigots around that you can "steal" from.
Regards,
Doug