My neighbour filed false cases against me, which were thankfully dismissed. Can I file a defamation case against them? Where should I file it: here in my city, or at the court where they filed the false cases?

Yes, you can file a defamation case against your neighbour for filing false cases. You can file the defamation case either in the court where the false cases were filed or in the court of your city, as long as the court has jurisdiction over the matter and the defendant.