I was hoping to find a site where I could find old games that are available to watch, specifically NBA and NFl. Any suggestions?
Finding old games is a relative challenge, and doing it will likely cost you some cash if you can do it at all (legally).
There does not seem to be a legal method to watch old NBA games. For classic NHL games the NHL offers a subscription service called "NHL Vault" for $5 a month. I don't know how complete the archive is, but it looks pretty solid.
MLB has a limited selection of old games online as well, though you may need an MLB.TV subscription. And the NFL offers a "game rewind" feature on their website for a fee ($70 a season for full access). The NFL archive only goes back to 2009 though as well as some "classic super bowls".
You can also try youtube, a limited number of games may be available there (or parts of them). The legality is possibly debatable there, but at least they comply with take downs etc.