I don't know how many days you will be there.. But I'll tell for 2 days.. Take a rental bike, it costs around ₹250...Roam around the French city.. Visit Aurabindo ashram and can go to Auraville.. Eat some French and Italian things. Take a bus and go to Picchavaram mangroves {don't miss it}.. If you have time then please visit Chidambaram natarajan temple.. It's awesome..And play in the beaches.. Go to the rock beach in the evening, take a wine bottle and enjoy your sip by looking at the sea..
You can book near rocky beach and spend an evening walking around the beach .you can go to matri mandir, a fantabulous place to see the inner globe of annai aurobindo. if u are vacating on Sunday then near the basilica church Sunday market is put where u can get all home things at cheap rates.
French COlony
Auroville
Pichhavaram Mangroves
Aurbindo Asharam
Sip a Coffee in the evening hours at Le cafe (White town)
Must visit Villa Shanti Restraunt
Try out Cafe De artes
Stay on Le Pondy (its right on the paradise beach)
Visit Natraj Chidambaram Temple
Plan an outing for Auroville Best thing to cover this is by scooty : Rent a scooty which cost approximetly 300 or less and go on exploring the city