The local tournaments have always been one of the things that really sets the FGC apart from almost any other competitive scene in video games. Having people run locals for something like DotA or CS is basically unheard of this at this point. Meanwhile, thousands of fighting games players gather to play each other offline every single week.
Finding them is not always easy, however. The nature of these events means that they typically don't get a lot of coverage and can't exactly advertise themselves too extensively.
To answer the common question of "where's local" UltraDavid compiled a massive list of events with the help of the worldwide FGC, and now you can easily check it out in a nicely formatted document.