Just in case someone else hits this problem and comes here looking for a solution:
After I upgraded to Yosemite, I was receiving errors when trying to build for Android. And I got errors when trying to open the SDK Manager from inside Xamarin Studio that pointed me to Oracle to download the latest Java 8 (which I did to no avail). Xamarin Studio would also just hang if I tried to close it after doing this!
Trying to open Eclipse also failed but pointed me here: http://support.apple.com/kb/DL1572. This updated Java 6 and fixed all the problems.