I've spent way too much time digging through different sites looking for Raph/Mikey content, so here's my take. Archive of Our Own is absolutely the main hub these days, especially for newer and more creative takes on the pairing. The tagging system lets you find exactly what you're in the mood for, from established relationship fics to slow-burn enemies-to-lovers AUs. It's also where a lot of the more nuanced, character-driven stories seem to congregate; you get less of the pure fluff or smut and more explorations of their dynamic.
FanFiction.net still has a massive back catalog, especially from the 2012 and 2003 series heyday. The quality can be really hit or miss, and the search is terrible, but there are some absolute classics buried in there that never got ported over. Tumblr is weirdly crucial too, not as a hosting platform but as a discovery engine. Writers will post snippets and links, and the reblogging culture means a really good fic can spread through the fandom fast. I'd start on AO3, use Tumblr tags to find recs, and then maybe brave FF.net if you're desperate for more content.