Safranbolu is in Central Anatolia.
Busses from Istanbul take about 6 hours and cost 20-25 YTL. Busses 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 busses are likely to let you off / pick you up. Once in the old town, everything is reachable by foot. Additionally, some intercity busses 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.
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.
Prices may vary depending on the season and the weekday.
Bastoncu Pansiyon & Kafeterya is one of the cheapest options in Safranbolu. It is clean and homely, with excellent meals. Dorm beds are 15 YTL a person, and rooms are 35. Breakfast is included. The owner speaks Japanese and English, and can help you plan your onward trip. Call them for a free pickup from the bus station. Phone (90370) 712 3411; Cell (0535) 642 1275.