Sure, about anyone can find their way to NYC, but how many of them can plausibly call upon the sorts of hardware and manpower resources the US military can? How many New Yorkers can plausibly provide big-ass robots or mech suits for the turtles to fight?
Uhhh... what? Where are you getting "robots or mech suits" from? The Turtles in their various incarnations generally fight ninjas, street gangs, other mutant therianthropes, alien invaders, or supernatural/extradimensional entities. When they do fight robots, they're generally either alien robots or the inventions of Baxter Stockman, a rogue scientist. And the latter are not particularly big; Baxter's best known for creating the Mousers, small but numerous robots with lethally sharp metal teeth.
As a rule, the Shredder is portrayed as the head of a massive criminal organization, sometimes behind the facade of a large corporation with abundant wealth and resources. However, in the first two live-action Turtles movies, he was more of an underground figure, a Fagin-like corruptor of youth organizing a street-level criminal gang. There's no requirement for a TMNT story to be on a massive scale, though they often are.