You'll find the government parks (local, state and federal) will have great space and general privacy since they are not trying to make a profit. The more a commercial park can pack in the higher the profit. The down side not all have full hook ups. Most will have water and electric (30 amp is pretty common) but just a dump station. Also sites might be a bit shorter but with a bit of planning shouldn't be problem.
With the coach you have you should be able to go four or five days on the tanks. Conserve water and you could push it to seven.