Miami's international airport is not very far from the city and beaches, and you can be in your hotel in about 30 minutes. Taxis into the city should cost between 20 and 30 dollars plus a 15% tip, although it is highly recommended that you rent a car.
For transfers from and to the airport to/from your hotel, you have the following services:
Arrival Transfer
Departure Transfer

Unless you're staying in South Beach and never leave your beach towel, Miami is not a walker's city and it can be quite a hassle to rely on public transportation. In fact, very few visitors can live without a car, as the city is so spread out. See the cheapest car rental rates here.