I can only suggest that you google
Dinan Hotels or
Dinan Accommodation or contact the local Tourist Information Office -
Office de Tourisme - Dinard might get you a response if you google it too.
Dinan is a beautiful town, but I don't necessarily think you'll find cheap accommodation there ... reasonable or fairly priced yes, but bargain basement, no. You might be better hiring a car and finding a GITE or a CHAMBRE D'HOTE in the countryside around it. Incidentally googling these words plus DINAN may also get you results.
Incidentally I think you might have made a little mistake in your post because you will be flying to DINARD, a coastal town, much loved by the Brits of yesteryear because of its casino and seafood. Dinan is about 30 miles inland down the River Rance. Dinard airport is in the village of Le Richardais. You might explore Dinard and St Malo for accommodation options too.