There is a Claudy in County Derry; on this map. It's shown southeast of Derry city (it's about 10 miles away), towards Dungiven (not on the Foyle). There is a River Claudy in Co. Derry. This is the first place I would think of when I hear the placename "Claudy", but is there more concrete evidence to connect the song with this place?

A "River Clady" is mentioned in versions of the Whistling Gypsy / Gypsy Rover. I heard it sung with a long A sound, unlike the pronunciation of the Donegal River Clady near Meenaclady (Mín a' Chladaigh), Gweedore (Gaoth Dobhair). Mention at this fishery site of a Claudy River in the same general area, perhaps refers to the same place? There is reference to the "Clady Banks" in the song "Green Fields of Gweedore", but also in this poem from the Finn Valley area further south in County Donegal. Clady, Co Tyrone is on the banks of the River Finn.
There's also a River Clady in Co. Meath.