Short answer: Promote your website to where your potential customers are. (We are talking about customers, meaning people who will pay or buy something from you, not visitors, who just people visiting your site.)
Long answer: There are many places you can promote your website. Talk about online - Facebook, Google, Pinterest, Instagram, Reddit, Forums...etc. Talk about offline? The places are endless.
But one concept in mind you have to remember, is to promote your website where your potential customers are. And it really depends on your business.
Because if you know where your potential customers are, and how they buy, you will know how to promote. Hence, it is not just going to Google or Facebook to promote.
1) I use Google SEO for my client's local businesses.
When people are searching for products and services in their area, they usually go Google. So optimizing my clients' site to rank high in Google is the 'promotion' method. With the right optimization, my clients are guaranteed constant stream of leads and customers from their area.
Do I use Facebook for this? Yes, but the conversion rate is lower. The time I show my FB ad to them may not be the time they are looking for the product.
2) I use Facebook Ads for one-time events and seminars.
My client want to organize a public seminar to teach people how to speak confidently on stage. This event is for salespeople, managers, and anyone who does speeches and presentations.
To promote this event, I use Facebook ads to target people who have interest in public speaking, speaking from stage, effective communication. They are people who want to learn more about speaking, hence, this event is for them.
3) I use Instagram for selling fashion items
My client has an online boutique, and she sell dresses, ladies' office wear...etc. I use Instagram to promote his website.
Instagram is the place where people show off pretty, cool, fashionable stuffs. Posts on Instagram are visually appealing, and it is easy to catch people's attention. People loves to show their #OOTD (Outlook of the day) and yes, these are fashionable people. And so, this is where you promote your website.
To sum it up:
Places to promote your website? Tons of it.