What drew hundreds of thousands of people westward in the late 1800's?

The prospect of cheap land and the gold rush.

Land in the west started out fairly cheap in that someone can buy acres of land for a couple of dollars. They were however suppose to stay in the area for a certain amount of years. However, gold was soon discovered in the west, and many people, thinking to strike rich, packed their bags and either traveled on trails westward, or got on ships and rounded cape Horn to get to Port cities located on the west.

So your answer is land, a new life, and gold

Hope this helps