This is a very important question that may affect the cost of your fountain. On most commercial fountains the backwash water must go to sanitary sewer and not to storm sewer. In some municipalities these sewers are combined, so check with the building departments prior to designing the piping.
In either case, there must be an air gap between the pressurized backwash pipe from the filter and the sanitary sewer. This is usually accomplished by discharging the backwash pipe into a tank that then has a sanitary connection in the bottom of the tank. We usually size the backwash tank to accept the entire compliment of backwash water from the filter that is, the filter flow x 3 minutes.