Taxis and buses are easy to find in Oaxaca, although everything is also within walking distance. Natives use scooters, cars, or buses. Oaxaca is big and spread out, expecially if you want to get into the countryside. Consider a private guide.

The central part of the City, where most tourists stay and where many of the main museums and other attractions such as the Zocalo are, is very walkable. There are many pedestrian only streets. Depending on your length of stay, you might never need to take a taxi, except to return to the airport. (Collectivos from the airport are very inexpensive and easy to find. There is a small ticket office right at the exit from the airport, near where one enters the main terminal from flights. The Oaxaca airport is small and easy to navigate.  Finding a collectivo to the airport is a bit more difficult for those not familiar with the system.)

There are many reasonable tours offered to area attractions and even a cursory walk around town will bring you into contact with tour companies. Talking to other travelers or your hotel/B&B can also help you determine what tours you might prefer. There are also collectivos (group taxis) and first and second class buses. Both bus stations are within walking distance from most accommodations in the centro area. Hiring a taxi in some instances can be very reasonable. Most B&Bs have taxi drivers they work with and can assist in finding reliable drivers. Walking at night in the centro area is safe and women can walk by themselves and feel secure, using of course all the normal cautions of any city. Oaxaca central city is probably safer than most.