Hampi servers the purpose well for a first time solo traveller. It's safe, easy to reach and heck of an experience. Try exploring Hampi along with Badami, pattadakal and aihole. But if you are looking for some peaceful nature time you can go to ooty.
If u love hill stations then you can choose coorg,wayanad,valparai,kodaikonal,sahyadri ranges hill stations if you love beaches,you can choose Varkala,dhanushkodi,pondichery if u r a nature lover go to Kerala road trip