I know that most published fiction doesn't emphasize the character's accents, but then of course we have our famous examples of stories that do. Mark Twain's Huckleberry Finn, at the very least. There are many different reasons to emphasize an accent. Most of them come down to wanting to emphasize socio-economic status or foreign backgrounds. Whatever. I'm sure you have your reasons, and if you don't, pretend you do for a minute.
If you were going to write a story where one or more of the characters have a pronounced accent, what would that accent be? What would be fun to write? What would be realistic for your story? If you decided to go all out and mimic the accent in your spelling, would that change your answer? Would some accents be too dang hard for you or your readers?