What is the farthest blueshifted object to our galaxy? Is it also roughly the limit where gravity will be able to overcome space expansion? In other words, we can only hope to get to there, or at least see them, in the very far future?
My impression is that, aside from the very rare galaxy that is moving towards us, only stuff inside the local galactic gravitational field can be blueshifted.  Written perhaps more clearly,  from spaceanswers , 


  Andromeda is not the only galaxy to be moving towards us. With the
  help of galaxy surveys, astronomers have found that around 100
  galaxies are moving towards us. Compared to the numbers of galaxies
  that we know of (hundreds of billions), blue-shifted galaxies are
  seemingly quite rare. Those that are moving towards us are either part
  of our Local Group, which means that we are gravitationally connected
  to each other, or they are found in the Virgo Cluster which everything
  in our Local Group is moving towards. The galaxies M90, M86 and M98
  are all in the Virgo Cluster and all show blue shifts.