Parking at the port is $20/day. It is a garage and looks safe.
There are a couple of places in downtown Miami. I think it is Premere parking that is $8/day and is a garage but very very tight. I parked at a fenced but outside lot for $4.50/day and while it seemed sketchy at first, I thought it was fine in the long run. I took a shuttle to the port for $7 which was supposed to be round trip but I couldn't reach the people when we returned and I just took a taxi ($13 including tip).
Some people also park at the airport, or at a hotel with a park and stay deal.
Nancy