(Wayback Machine links preferred where possible)
I personally have a lot of nostalgia for serebii.net (est 1999), the Pokémon fansite two years older than I am. The Wayback I chose was from Dec 2014, but I'm pretty sure the site's whole layout is still identical today, just with three extra Pokémon generations in there. I was using this website for everything Pokémon since at least 2010, maybe even 2008. Basically, from the moment I had both the ability to read and to use Internet Explorer without adult supervision.
It had everything a complete child struggling through Pokémon Diamond with one over-levelled starter, five HM-laden Bidoofs/Starlys, and two Scholastic Book Fair Ultimate Pokémon Handbooks could ask for. Walkthroughs, secrets, cheats, explanations of how to actually play the games and not just mash "A," even hot goss about upcoming in-game events and news about the next games. Probably helped inspire me as a child to buy a used GBA and get my mom to eBay me copies of Pokémon Yellow (legitimate) and Sapphire (unknowingly bootleg), since I wanted to go back and experience the Pokémon games that came out before I started. (Gen 3 quickly became my favorite.) I don't know if serebii is my favorite per se, since there's a lot of great websites out there, but it's a good example of the kind of nostalgia I'm looking to bait.