If you have a felony warrant in Indiana and you get arrested in Nashville Tennessee do you have to be extradited?

You won't have any 'say' in the matter. TN will notify IN they have you in custody and if IN says they want you back badly enough, THEY will initiate extradition proceedings.

All US states and territories honor each other's requests for extradition - there are no 'safe-haven' states - It is impossible to know with certainty whether a particular state will choose to extradite you for a particular offense, or not, there are simply too many variables. It may depend, in part, on the offense and the seriousness of it, and/or how badly they want you returned - most states WILL extradite for felony offenses.