Being a city with many undulations, manual rickshaws have disappeared from most of the city. Autorickshaws are used by many for travel within the city. One can hail one down from anywhere in the city. (It would help to know the distances to avoid being cheated.)
The safe bet is public transportation. Although there is room for improvement in convenience, comfort and frequency, the APSRTC city buses will get you safely to your destination.
The Vizag Metro is being planned and Vizagites are thrilled that the Metro Man, Mr. E Sreedharan himself has been tasked with overseeing this project. The Detailed Project Report (DPR) is scheduled to be completed by the end of June 2015.
Visakhapatnam being unique in that most people living in the city usually can reach their venues within 6 kilometers, taxis (cabs) had not really taken off earlier. Now, Ola Cabs and Uber have had a presence for over 4 years. Usage is still low since the fares have remained relatively high keeping price-conscious customers away. Earlier, one could get a cab for approximately the same fare as an auto without the hassles of bargaining and price gouging.