Miami International Airport: Use the free MIA Mover to the Miami Intermodal Center, then take Metrorail’s Orange Line south to Coconut Grove station (about 20 minutes on the train; roughly $2.25). The station is west of US-1, not in the restaurant-and-bayfront core: allow another 20–30 minutes on foot or 5–10 minutes by rideshare. A rideshare straight to Coconut Grove is usually faster with luggage—about 20–35 minutes, but much longer in rush hour, and roughly $25–45.
Fort Lauderdale–Hollywood International Airport: Only use FLL if the airfare saving is real. Rideshare to Coconut Grove is usually the least painful option: roughly 45–75 minutes depending on I-95 traffic and about $50–80. The cheap route is the airport shuttle to Tri-Rail, Tri-Rail south to the Metrorail Transfer station, then Metrorail south to Coconut Grove; budget 90 minutes or more, plus the last-mile ride from the station.