The Gautrain runs between Pretoria station and Hatfield (for the embassies and university area) with several stops including Menlyn. It's by far the safest and most reliable option for the central corridor.
Taxis are metered (Uber is widely available and preferred by most visitors and locals over street taxis). Do not flag down unmarked vehicles. City buses cover the main arteries but schedules are unreliable. Most of Pretoria's key attractions are spread across the city and not easily connected on foot — a car or Uber is the practical option for a full day of sightseeing.
Walking in the central city (Church Square area) is fine in the daytime. Avoid walking in the CBD after dark. The Arcadia and Hatfield suburbs are safer and have more restaurant and bar options for evenings.