Safest / Cheapest Way to Get around BRASOV in Transylvania / Romania

We want to visit Bran Castle , Brasov Zoo and the Libearty Sanctuary

We plan on flying directly to Brasov and staying in Brasov, to avoid the long travel from Bucharest

But we see a lot of warnings online about unregistered taxis and those who try to take advantage of travellers, (Saying one price, then try to charge you x10 when you get there)

What are the safest and cheapest ways to travel around Brasov?

We would need to go from Brasov airport into Brasov , and also go from Brasov town to the castle, zoo , bear sanctuary etc.