Safranbolu is in Central Anatolia.
Buses from Istanbul take about 6 hours and cost 20-25 YTL. Buses from Ankara take around 4 hours.
Dolmuses regularly drive the 2 km between the old town (Çarşı) and the new town center, which is where buses are likely to let you off / pick you up. Once in the old town, everything is reachable by foot. Additionally, some intercity buses might drop you off in the nearby steel down of Karabük. From there you'll have to find a dolmus into Safranbolu.
Safranbolu is famous for its Ottoman houses, and qualifies as a UNESCO World Heritage sight.
Safranbolu Baglar Saray
Take a look (and a tea?) inside the Cinci Hanı, a massive hotel in the center of the old town. Wandering around the city you will take in much, but to see inside the houses, head to one of the historic homes open to the public. Kaymakamlar Müze Evi is located just above Bastoncu Pansiyon, to the south-east of Cinci Hanı. Keep walking up the hill, and take in some beautiful views.