There are shuttles from both airports in Istanbul. I would stay in Sultanahmet if you are a first time visitor as easy to then walk to the sites you are likely to want to visit, Blue Mosque, Aya Sophia, Topkapi palace, Grand Bazaar, Yerebatan cistern. Been told very recently by some people who went that the ceramic museum is amazing. Not sure but think on the Hippodrome area close to the Blue Mosque? Maybe someone else can say if this is correct. Lots of hotels in this area of Istanbul, sure some thing on here if you search. Getting around is easy, either by foot, by metro or by taxi. Enjoy, it really is an amazing city!