With full hindsight, Kelly Ayotte, Bob McDonnell, or a top foreign policy person(say, Condoleezza Rice or Zalmay Khalilzad) would work very well.
To answer the question, Romney wanted someone who could help him unite the Tea Party base (while having the necessary experience for the job, so he could use the experience argument against Obama), he didn't want someone seen as being 'too establishment' like himself.
Believe it or not, at the time, Ryan was quite popular with the base. Breitbart praised him day in and day out.
^There was also the WI element as the above poster points outI don't know why Ryan wouldn't be popular with the base ... the fact that some now call him of all people a "RINO" is truly telling of the Breitbart crowd.
