All characters have an accent. I don’t want to hear any of this ‘but they’re neutral, they don’t have one’, because they do. Even if it’s your accent, then they have one.
But that doesn’t mean you need to alter everyone’s speech.
Only the characters with the stronger accents need to have it changed, for example, the Southern US, y’all replaces you, and the tendency to leave out the odd sentence connective increases. Londoners drop the G from the end of words and use double negatives more often. Eastern Europeans use V instead of W in speech.
Try not to include too many accents though, it’s very rare that multiple accents encounter each other in everyday scenarios, with the exception of large cities.
-C