From Hue, local buses take about 3-4 hours, and cost 80,000 dong (Sept 2012), departing from the Northern Bus Station. Tourist buses cost 4-5x the price: ie., Sinh Cafe (400,000d), Mandarin Travels (300,000d).
Most buses will drop you off on Hung Vung, which is closer to town than the bus station. You can easily walk to a hotel from Hung Vung.
The Reunification Express makes a stop in Dong Hoi. The train station is 3km from the city center