The beauty of BRRRR investing is that there is inherently no best area as it will depend deal to deal. I've personally bought places in areas I never thought I would invest just because that's where I happened to find the deal. I've also sold properties in areas got wouldn't expect. I've seen a $450k condo in the Gold Coast he bought and rehabbed to the point of being valued at around $1m (with a little over $300k of work). If you're dealing with a low budget (I know you aren't) then there are specific areas that can be good but with a higher budget, you'll find that there are places all over that can be good.
Personally though, if I’m dealing with $400-800k, I would consider buying a small multifamily place in the south Logan square area and converting it to a single family. I’ve seen those types of places (old two flats) be bought in the $400k range, get completely gutted and redone on the inside and then get sold for around $1m as a beautifully renovated single family.
But there are tons of possibilities in that price range.