The French Quarter is small enough to walk entirely — most sights are within 15 minutes on foot. Bicycles are the classic way to get around Pondicherry and can be rented from several shops near the ashram for a low daily rate; cycling through the quiet streets of White Town in the early morning is genuinely enjoyable.
Auto-rickshaws cover the broader city and the ride to Auroville or Paradise Beach. Agree on a price before getting in; there are no meters. For Auroville specifically, several guesthouses can arrange motorcycle or scooter hire, which makes moving between Auroville's spread-out communities much easier than relying on autos.