I've included a link below that may answer many of your questions. My opinion is that Riverdale and near Fordham University - Bronx campus - would be promising locations to purchase. Are you looking to purchase for investment or to live?
If you have the opportunity, you should walk/drive around the Bronx to determine where you would like to purchase. There are so many variables to take into account when purchasing that I recommend you speak with a Realtor to help you determine what neighborhoods meet your goals and budget. Feel free to contact me or Adina Greenberg. Adina also posts answers on Trulia and lives in Riverdale-south Bronx.
Hope this helps.