Need advice on layover in Istanbul

I am looking to travel with my family (my husband, 2 small boys, and myself) to Italy next March to visit family.  So far the best airfares on the web are thru Turkish Airlines, but coming and going require an overnight layover in Istanbul.  I've always wanted to visit Istanbul.  Although this isn't actually 'visiting' Istanbul, but it would require us to stay somewhere, as where staying in an airport for 19 hours with two children does not sound appealing.  Does anyone living in Istanbul have any suggestions on what I can do, who we could contact to get help from the airport, perhaps stay with, and see a sight or two before being taken back to the airport the following day.  We are willing to accommodate financially for this help. Thanks and God bless!