This is the mosque that most visitors see first. In many cases it's the only mosque that they see. Built on the orders of Sultan Ahmet 1 and still bearing his name, the Blue Mosque of Sultanahmet dominates, in conjunction with Aya Sofya, the Hippodrome area which has always been the center of the city. Mehmet Aga was the architect and the Mosque took 7 years to build. The Sultan himself joined the builders on several occasions to lend a hand but died within 12 months of its completion at the age of 27.
It is difficult, and probably pointless, to attempt to avoid comparison with Haghia Sophia and certainly futile to say which is the most impressive structure. I have my own opinions and you will arrive at yours I'm sure. One key difference is that the Blue Mosque is a living place of worship and carries out this function continually. As a visitor you will be ushered in through a side gate and your access to the Mosque is carefully controlled. If you're going to be spending any time in Turkey and want to see Ottoman or Selcuk art then you're going to have to get used to visiting mosques. It's really not very scary. If you dress appropriately you'll feel more comfortable, but if you don't you will be provided with something to hide behind. A word of caution, in the winter the mosque is very, very cold so you'll want to wrap up warm (several pairs of socks is probably a good idea). Due to the status of the building as a functioning mosque there's not much of the building that you're free to explore. The interior is very impressive though many commentators feel that the elephantine columns lend a heaviness which detracts from the overall feel. Highlights include the fine Iznik tile work on the lower parts of the walls, the carving and inlay work of the doors and windows and the carved stone of the mihrab and mimber.
Istanbul certainly has finer and more delicate examples of Islamic devotional architecture but there is something to be said for the scale of the Sultan Ahmet Camii. Don't forget to take in the buildings surrounding the mosque itself and forming the kulliye, the foundation built at the same time as the mosque and comprising a primary school, medrese (seminary), hospital, public kitchen, karavansaray and market. Not all of these buildings survive but those that do give an idea of the scale