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Back to the Future!
There are not currently a wealth of resources that can help you visit the internet as it used to exist. That being said, there are some that can help you discover online resources from the past.
Luckily, the Internet Archive saw fit to create The Way Back Machine. The Way Back Machine allows users to search through snapshots of the internet from the past. It should be pointed out that not every page is present nor is it updated daily. As such, it is unlikely that you will find obscure sites as they exist 20+ years ago. However, prominent sites are accounted for and snapshots exist for all sorts of things and all sorts of dates. For example, JHU.edu, as it existed in 1997, is present and accounted for on the Way Back Machine. You can check it out HERE.
The Internet Archive also collects a great variety of online resources and makes them available to users.