As Second_Mate notes, plenty of hotel rooms were needed to host the small army of politicians and bureaucrats that had fled Paris.
But there was also a strong sense in which Vichy was a 'negative choice'. The key cities of the Unoccupied Zone were all unacceptable: Marseilles was too unruly and close to the ports; Lyon was the Third Republic fief of Radical politician Herriot and had a strong working-class tradition; ditto with Toulouse (under Sarraut); Clermont-Ferrand was a perfect central location, and did very briefly host the fleeing government, but had too little accommodation and was Pierre Laval's stronghold.
So not only did Vichy have plenty of practical comforts, it also lacked a sizeable working-class population or strong Republican traditions. A suitably bourgeois surrounding for the National Revolution. And, of course, this was originally judged to be a temporary measure: the assumption was that the government would quickly return to Paris.
Sources:
Julian Jackson: France: The Dark Years
Robert Paxton: Vichy France
Two main reasons, apart from it being fairly central to the rump of France, geographically. As a popular Spa town it had very many hotels, such that it could accommodate government offices without causing serious dislocation. It also had very good communications with good and telecommunication rail links.