your question is so simple. You can file petition any one of these three places.
1. Where marriage was solemnized? (your hometown)
2. Where partied resided together (Bangalore)
3. Where wife is residing at the time of filing the petition (Bangalore). So, you cannot file petition at Chennai, as it is different place from the place where marriage was solemnized. If you file your petition in the place where marriage was solemnized (central district of T.N.), your wife may appear there or seek transfer of case from that place to Bangalore or to the place, where she is presently residing (if it is different from Bangalore). But this transfer is from one State to another State, she has to approach the Supreme Court.
Next question: If you do not know her present residential address, try to find out her official address and serve the divorce petition to both the places. It is always advisable to have a divorce decree out of contest divorce case than ex-parte decree.
