Patna originally known as Pataliputra is known as cradle of empires which upholds lot of Spirituality. There is lots to explore. Bihar museum
Golghar
Kesaria stupa
Patan Devi mandir
Japanese peace pagoda
Sanjay Gandhi botanical gardens
Kumhrar park
Gandhi ghat.
Agar aap proper Patna ghumne ki baat kar rhe hoto aap Bihar Museum , Golghar , Patna Zoo , Gyan Bhawan , Bapu Sabha ghr , Gandhi maidan , NIT ghat , ye saare jagah explore kar sakte ho... Or agar Bihar me patna ke alawa kahi or explore karna ho aapko to aap Nalanda , Bhagalpur , Sasaram ,Rajnagar Madhubani , Rohtas ye sb jagah explore kar skte ho jaha aapko waterfall or Tomb wagera milega ..
Bro it depends upon the theme of tour you are looking for, but besides places in Patna suggested by other friends you may also cover Patna Saheb Gurudwara, Nalanda (80 km from Patna, a UNESCO World Heritage Site), Mahabodhi Temple (120 Km from Patna, a UNESCO World Heritage Site) and Baidyanath Dham (one of the 12 Jyotirlingas in Devghar, about 250 km from Patna).