I'm guessing the apartment must have been built or renovated very recently, because the condition really was pristine. Every surface practically shone. It beat the living hell out of our own apartment, for sure. The design was modern and luxurious - the little stone alcove with a green lamp reflected in the shining floor tiles below was a cool touch. Couldn't have asked more from a fancy room in a fancy high-rise hotel in some European metropolis. It had air conditioning, free WiFi, satellite TV, a kitchen corner with a fridge, and a comfortable bed - anything we wanted and/or needed. Also, the location is as central as it gets: 5-7 minutes walking time to the Riva promenade, Diocletian's palace, the Bačvice beach and the harbour.
Margareta, the hostess, is truly an absolute gem. When we arrived she sat us down with a map for 30 minutes and gave us the full Split rundown - restaurants, sights, island ferries, bike rentals, the Marjan park - anything you could possibly want to do, and finished by giving us a bottle of local liquor. We were given a cell phone with her number on it, which we were free to bring along to call her if we had any questions.
So, to summarize - an impeccably clean and modern apartment in the heart of Split, with the kindest, most good-hearted hostess you'll ever meet. We'll stay at no other place if we come back, and we recommend it to everyone.