Konya's sights divide neatly into two clusters. At the centre is Alaeddin Hill, the ancient citadel that Konya has been built on top of for three thousand years; the Seljuk Alâeddin Mosque sits at its summit, with the Karatay Madrasa and Sırçalı Medrese (now museums of Iznik tiles and tombstones respectively) nearby. A ten-minute walk east is the Mevlana complex: the green-tiled mausoleum of Rumi, the founder of the Mevlevi order, and the most visited religious site in Turkey after the Hagia Sophia.
Around these are scattered the Ottoman mosques — Selimiye, Aziziye — the Ethnography Museum, the Archaeological Museum, and the old bazaar around the Bedesten. A serious day or two will cover everything; if you have only an afternoon, the Mevlana Museum is the unmissable visit.