It's hard to guess at a cost to repair the leak without being able know what exactly is the source of the leak, hose a frost plug ? The way an automotive shop would locate the leak is by removing the radiator cap and attaching an adapter that screws on in place of the radiator cap. Something that looks like a bicycle pump with a pressure gauge attached to it is used to "pump up" pressure to simulate pressure generated when the cooling system is at operating temperature, the leak is then found sometimes it is obviously leaking from a coolant hose or cracked housing, failed gasket or water pump, sometimes the engines cooling system needs to be inspected from below or inspected using a mirror and flash light. If the coolant loss is still evasive dye can be added to the cooling system that may indicate the source of the leak. A mysterious coolant loss may even be a sign of a head gasket that is not sealing well.