For just two nights, you might consider the Hôtel Kyriad Dijon Gare. It's a chain hotel and rather plain, but it's reasonably priced and very well located near the train station. It's a short walk to the Porte Guillaume arch and Rue de la Liberté, which has lots of shopping, some half-timbered buildings, and leads you to the beautiful Place de la Libération and the palace of the Dukes of Bourgogne (which houses the recently-remodeled and re-opened Musée des Beaux-Arts de Dijon). It has air conditioning, I would suspect you could get two twin beds (especially if you ask in advance) and, while the rooms are French small, they're clean and updated.