I'd book a hotel in the city, not near the airport. You'd have more choices, and the train doesn't leave from near BKK international airport anyways.

The Chiang Mai train leaves from Hualamphong and there are plenty of hotels in that area. It's also a business district, so no worried about wandering around the area during the day.

Finally, you're better off leaving luggage with the hotel and picking it up shortly before heading to the train station.