A journey we took starting from Islamabad. We opted for the reliable Daewoo bus which costed us just $3/person to reach Murree in about 2 hours.
Be prepared for the travel and it has a lot of twists and turns. On reaching Murree, we settled in and walked around the Mall Road area and went down the less visited route to explore the locals there.
The next day, we got ourselves a private car for just $18 for a whole day trip to Nathia Gali and Ayubia. For us it was the amazing journey to these places and back -with stops on the way to take pictures and to enjoy the amazing landscape around us. Overall it would cost you $25/person/day in case you are 2 people including stay, food and travels.
As for safety, this place is one of the safest places to go in Pakistan, especially Murree, being under control of the Army – so its super safe.