We stayed at the Homewood Suites Miami Airport Blue Lagoon in May 2015 and had a 2 bedroom suite for about $150 a night. It was amazing. They included dinner (with wine) and breakfast each day. We also had fast internet. There is a Publix at the end of the road and their shuttle will take you there for free as well as to and from the airport for free. It was clean and the staff was wonderful.
To get to the airport the next day, a cab was going to cost us $50 or so...we could have used the shuttle to go to the airport to catch a flat rate cab to the port for $24, but since we had 9 bags and a 4 year old, we opted to use Uber. Since it was my husband's first Uber, the ride cost us $4 total for a large SUV. You are not required, by law, to use a child safety seat in any hired vehicle in Miami-Dade. I contacted local law enforcement prior to going, so we buckled our 48 pound kiddo in the back seat with us and kept the booster packed in the suitcase to be checked at the port.
Edit: We boarded on a Friday morning. There was traffic, but I think it took us about 25 minutes to get downtown to the port. So it was worth the savings and the ability to shop the night before at Publix and have 2 bedrooms and a kitchen and our meals all taken care of to stay out by the airport.