There is a train on Crete? Also don't misprize the distances on Crete. One side to the other is 300 km, 4,5 hours by car. Even to Sitia you will need 2 hours.

Taxi will be around 90 € per way, extra charges for laguage aren't uncommon in Europe. If you really don't take a rental car you will pay a lot fot taxis and minimize your fun. Also with 3 days concentrate on the region near the hotel. It's not the most attractive, most sights are at least a 30 minutes drive away.