I went to Safranbolu in December & it was really one of those enchanted trips that I'll always cherish. Here is a website to help you find accomodation (they have links to the various hotel's home pages, where applicable):
http://www.safranbolu.gov.tr/safranboluda_konaklama.htm
I stayed in a restored home called 'MEHVEŞ HANIM KONAĞI.' It was really cool (breakfast was excellent), but I saw all of the rooms and none of them will be suitable for a family (very tiny).
I recommend staying in the Çarşı area - the heart of Safranbolu.
If money isn't an issue, Cinci Han has suites:
http://www.cincihan.com
If you have time, try to do some research about the fascinating functions of a traditional Safranbolu home. Also, try to see Bağlar - this is where Safranbolulites would summer (as it is higher and cooler). Also the aqueduct (Incekaya Su Kemeri) should be on your list. Will you have your own car?
If you ever want to get to get together for the lowdown and to see photos, you can PM me. I live in Fenerbahçe so it shouldn't be hard for us to meet.
Have fun! - I am jealous!!!