West you will find the courthouse and the feared overtown -- which as I mentioned elsewhere -- isn't the safest of areas.
Brickell is a short (15minutes or less) walk. There you will find better restaurants and droves of young urban business professionals who probably work in some form of consumer banking.
Wynwood is close, but you can't walk there because you'd have to go through Overtown which is, again, a really scary place to be even during daylight hours. It's full of artists , trustafarians, and some tech people. But mostly hipsters.
To get to any beach you will need a car.