6k? Are you buying a house?
I had a flight from the airport at about 6am, and my hostel was in Miami Beach, so I decided to do what any sane person would have done - to walk, as I didn't want to oversleep and I didn't want to pay for a taxi.
So I started walking at about midnight on a Saturday night. After I had walked for about an hour - I had just crossed the bridge to downtown Miami - a taxi stopped and offered me a ride to the airport for $20. No thanks, I didn't come here to spend my life savings on taxis (I didn't say that, that would have made me sound very poor which I was but that is a bit stigmatized in the US).
I walked for another four hours through what I think were very dodgy areas as they coudln't even afford street lights until I, exhausted and with my feet slightly hurting, saw the lights of the airport. Unfortunately, I got completely lost and went into the terminal for freight airplanes. Finally I gave up and asked one of the airport workers to call me a taxi (I was now completely sure I was going to miss my flight). The taxi turned up and drove me around the whole airport and I arrived a few minutes before checkin closed.
Price? $18, + $2 in tip. Five hours well spent and got to see the "real" Miami (at least I think it was). And before anyone checks the distance between Miami Beach and MIA on GoogleMaps and points out that it shouldn't have taken me five hours, I just want to tell you that I had a huge bag.
Nikki Beach is fairly nice and Washington Avenue too, and the basketball is good too if that's your cup of tea. The weather is brilliant all year around. Other than that, I thought it was overrated.