You could start with Chennai capital city that is well connected to many parts of TN. Now with pre monsoon setting in many parts of Tamilnadu
Pollachi
Tirunelveli
Rameshwaram and Kanyakumari Madurai and Kodai
Coimbatore and Ooty
Karaikudi Yercaud Kolli hills
Valparai Salem are some best parts of Tamilnadu to visit with family.
Hello, Chennai, The great chola temples, Pondicherry, Yercaud, Yellagiri hills, Madurai, Vellore Lakshmi temple etc are best for family trips. Happy Travel!