George Best Belfast City Airport is just three miles from the city centre. In your rental car, turn right out of the airport onto the A2 and follow it to the turn off for central Belfast.
Please note that this is different from Belfast International Airport, which is located 18 miles from the city centre. It would take around 30 minutes to drive to the centre of town if you take the A57 route then get onto the M2 from Junction 5.