How can I get people to visit my website without using social media?

It depends what your site is about really, but here are a few ideas:

• SEO (Search engine optimization) - Doing things to improve Google's perception of your site, so that it ranks highly for relevant search terms.
• Word of mouth - the traditional and time-tested method of getting people to visit
• Links - Getting other websites, bloggers, or web properties to link back to your site can be a big driver of traffic. It also improves your SEO if done correctly, because search engines like Google take links pointing to your site into consideration.

Out of curiosity, what's wrong with social media? It can be a option if done correctly!