Hey Anand, for Architecture you need to visit tanjaur srirangam
madurai meenakshi temple for Beaches chennai
Karaikal
Pondicherry
rameshwaram and Dhanuskodi
Kanyakumari for hill stations Ooty
Kodaikanal
Yercaud doddabetta
Connor
horseley hills Start from Ooty and then via chennai and then to tanjaur ... madurai and Pondicherry and Rameshwaram and lastly end your Trip in Kanyakumari... Plan your own itinerary with these Places... you can always ask your queries in Tripoto forum here ... Happy Travelling Bro!!!
Visit Chennai and mahabalipuram.. Then to pondicherry and if interested in history or weaving.. you can go visit kancheepuram.. if interested in hill station then do visit Ooty, kodaikanal, yellagiri n so on.. beaches.. kanyakumari
For 9 days you can cover not only Tamil Nadu but also near by states like Karnataka or Kerala also.
In Tamil Nadu Madurai, Kanchipuram, Mahabalipuram. Then you can also visit Pondicherry. Now if you want to to go to Karnataka you can try Gokarna, bannerghat etc. Or you can try back water in Kerala