If you are talking about going and coming back in the same day, you are in for a challenge. There is no real easy way, as they are in separate counties, so separate public transportation systems.
You could take a cab to tri-rail ($20?), take tri-rail to metro rail, to metro-mover, then a taxi across the bridge ($15-20?) into SoBe.
If you are planning late night activities, trains probably won't run.
I would look at a car service that typically charges $2 to $2.50 a mile. Probably cheaper than a taxi.