In Tilraukot you can find the ruins of the ancient city Kapilvastu which was the capital of the Sakya kingdom that Gautama Buddha was the prince of. If Tilraukot is really the ancient city of Kapilvastu is controversial. Some believe Piprahawa in India is the ancient Kapilvastu.

There is a museum that shows coins, jewelry and pottery from between 700 BC to 400 AD.

Sources: 

Locating the lost kingdom of Kapilvastu - The Himalayan Voice

In the centuries after Buddha's death 3 main Buddhism streams developed. Buddhism  before the division into verious branches is called pre-sectarian Buddhism.

The city of Patan south of Kathmandu in the Lalitpur district of Nepal has a big stupa on each of the wind directions of the city. The stupa's are said to be erected by the mighty Emperor Ashoka who made buddism his state religion spreading the religion all over northern India.

The buddha says that all life has suffering and unhapinness because of craving and attachement to various things. Like a house, friends, a car, personal belonings, good health, a happy marriage life etc, etc.

If we want to end our sufferings we have to reach nirvana. To reach nirvana the Buddha teaches an 8 point path we should live by:

On Buddha net you can find a dialogue between the Buddha and the Brahim Sundarika Bhâradvâja about bathing in rivers. The Buddha mainly says it is importent to prevent creating sins by being a "good" human than washing away your sins in Holy rivers. According to the gospels Jesus also was against bathing to wash away your sins which was done by the Pharisees. 

You can read the full article here; True Purification - Buddha Net

Lumbini in the plains of south Nepal is the birthplace of Gautama Buddha one of the four major pilgrimage sites for Buddhist. Buddhist pilgrims from all over the world come to Lumbini that has been a world heritage bij UNESCO since 1997.