Way too early to tell how this will turn out. One thought, why not have her run for VP? Problem is, Hillary was elected to the Senate, so she has been through a campaign. America may be more ready to elect a woman as VP than for president. All that said, she is definitely in the top 10 of my list for who I'd want to represent us as a nation.
Nobody 'runs' for VP. The choice of running mate should be up to the presidential candidate.