I have never heard of being charged to anchor but sometimes anchoring is prohibited. Most places have a maximum amount of time that you can anchor there. Personally, I much prefer to anchor and have spent well over 1000 nights on the hook at this point. If you are counting on anchoring all the time, make sure that you have ground tackle that will allow you to anchor in some less protected areas because there is no room to anchor in the good harbors in certain parts of the coast.
If you are leaving the boat for a while, you might consider renting a mooring. It is also likely to be closer to the dock making it easier to move supplies.