Royal Oak is the gay area, Southfield is more affordable and nearby.
If you want to be close to the city I would suggest Dearborn, you'll also be close to Grosse Point. You must have a car as I'm sure you already know! For God's sake Buy in the city if you can, don't miss this chance but don't host clients there because they'll afraid to go to see you at night. As we all know guys there hate looking for parking so wherever you live/host make sure there's parking right there or they'll freak out thinking they're going to park 2 blocks from you.
You have a $2 bus connecting DTW with Downtown Detroit (261 bus) and going right through Dearborn, that will save you shuttle/uber and airport parking if you live in Dearborn.
Btw get ready to fly only Delta.
Good luck!