Varanasi

Gaya - One of the most sacred places to do Pind Dan funeral offerings for the benefit of the soul of the deceased

Sarnath - One of the most sacred places for Buddhists, known as the place where Lord Buddha gave his first speech after his enlightenment.

Ramnagar Fort
historical royal residence and museum across the Ganges
Chunar Fort
ruins of battlements and ancient settlement 15 miles from Varanasi.

Agra - the next point on the tourist "Golden Triangle". Buses and trains, including overnight trains, leave several times a day.

Nepal - buses travel to the Nepali border where you can transfer to Kathmandu and Chitwan buses. Most buses go via Gorakhpur and can take 8-12 hours, or there are daily flights. There are a number of travel agents in Varanasi which will sell you tourist/AC buses to Kathmandu or Pokhara. Avoid these services especially the operator Paul Travels because they are not actually tourist buses. Instead, they are actually the local, public buses and once you get across the Nepal border, they will try to get more money from you.