If you can visit the site, then by definition it is free. No site can trace you back as an individual user and send you a bill. You pay your local service provider. They in turn pay for the regional infrastructure to be maintained. No distance charges.
Electronic mail is one channel.
The World Wide Web is another channel. The Internet is the term for all of this together. Modems at Service Provider. Some points to note Once through the front door of your service provider, the Internet is just one thing, ie whether you send mail or get information from a site around the corner, or around the globe, there is no real difference. You don't pay anymore, and there is nothing others can do that you can't do.