To find out how long Cristina's exile from Seattle Grace will last, read more below:
The hospital scenes at Mayo were filmed at the House Research Institute (pic above), and according to an industry article about location scouting, it seems that Cristina will be absent from Seattle Grace for four episodes:
Our set design team dressed the facility with fake snow there, to give the place a 'Minnesota feel,' since the Clinic was meant to be located in a Northern state during winter. [...] We shot there four different times in the past month, for four episodes that will be airing during the new season of the show, since one of the characters moved away."
We are looking forward to watching the four episodes in which the House Research Institute will be starring on network television, when they air this fall!"