Many city breaks to Riga already include transfers to your hotel from the International Airport at Jurmala, although if you have not booked these in advance, getting into the city centre is a simple matter of either catching one of the regular bus services or hailing a taxi. The city centre has an extensive tram network to get you around easily.
Unless you plan to leave the city centre, hiring a car is not necessary in Riga, however should you be staying in the country for longer than a few days, then it is a good idea to arrange car rental in advance of travel in order to make seeing the sights easier.