Most of the hotels near Dubai Airport run a free shuttle to Terminals 1 and 3. Check the pick-up point and the hours when you book, because they vary and the ones we found are the hotels' own claims.
Hotel shuttle
Grand Mercure says its shuttle runs 24/7 for Terminals 1 and 3. ibis Styles says drop-off 24/7. Premier Inn runs about every 30 minutes. Element runs at fixed times. Others do not publish a timetable. None we checked serves Terminal 2.
Metro
The Dubai Metro Red Line has a station at Terminal 1 and at Terminal 3, and Al Garhoud and GGICO stations near the hotels in Garhoud. You need an NOL card. Trains run about every ten minutes and stop around midnight, so the Metro does not help with a late arrival or a dawn flight.
Taxi
Metered taxis start at Dh25, about AUD 10, and wait outside arrivals. A ride from the airport to a hotel in Garhoud is short. Dispatchers may steer you toward a black limousine; ask for the metered one.
From Terminal 2
Terminal 2 has no Metro and none of our hotels runs a shuttle to it. Take a metered taxi.