Hey, I am studying in Varanasi from last 5 years (BHU). Best location to book hotel is Near Lanka,Assi ghat or Godowolia. And if you are looking for budget stay,there is a Zostel in Godolia near PDR cinema (Rs300 for one person,24 hours open,drinks allowed,they play daily one movie for backpackers at night). Google it.
Things to do in Varanasi : 1) Sarnath (Take a auto from BHU main gate or Lanka,Rs 50 per person) 2)Temples lik Old Vishwanath temple,Sankat Mochan ,Birla mandir. 3)Evening Aarti at Dashashwamedh Ghat. After aarti walk from Dashashwamesdh to Assi ghat ( it will take 20 minutes. Most of the ghats of varanasi will be covered.) 4)Wake up at 4:30AM and go to Assi ghat and see morning aarti and sunrise.After that take a boat ride that will take you across all the ghats (Rs50 in share boat ) 5)You can also go to Devdari or Rajdari waterfalls if you have more days. 6)And for the delicacies try Bhaang Thandai (In godowolia),Non veg at Shah chicken (nayi sadak in Godowolia),Kerala cafe (Bhelupur), Paav bhaaji (at assi ghat), Kullad vali chai (At Kashi cafe at assi ghat),Lassi from pehelwan lassi (Lanka). Try every dish. Hope this would help you.