Summer is definitely a better time to go apartment shopping in Miami. In the winter, the city is full of a lot of its part-time residents, which makes both the city and the rental markets overly crowded. If you start shopping anytime after April, you should be well positioned to find an apartment.
Miami is a city where there is often a little room for negotiation when it comes to rent prices and the terms of your lease. For instance, many landlords will ask for first and last months rent, as well as a security deposit. Don't be afraid to try and negotiate a little regarding these terms, as most landlords here will be used to it.
You can get basically anywhere in this large city using public transit. The bus system is very comprehensive, and also connects with lines serving more outlying districts. For getting around even more quickly, you can hop on a Metrorail line if you're travelling somewhere served by that system.
Boat tours in the Miami area are fantastic, and include open water tours, coastal tours, and everglades tours. Time in Miami wouldn't be complete without some time on either Miami Beach or South Beach. Sports fans can catch the Dolphins, the Marlins, the Heat or the Panthers. The nightlife in Miami might be among the best in the country, but the lines can be long and cover charges high if you want to go to a true nightclub rather than a bar or pub.