My wife and I stayed at House Dama for a long weekend break, and I cannot recommend it enough.
It is nice and central, with only a 5 -10 minute stroll to Diocletian's Palace, the sea front, and all the wonderful things Split has to offer.
The property itself is immaculately clean and beautifully decorated in a tasteful shabby chic style, that is cosy, welcoming and full of character.
Although small, the apartment has everything you could possibly need for a short, or even longer break.
The bedroom ceiling is low but it so suits the house, and only adds to it's charm and character. However, this is accessed via a spiral staircase, so may not suit a less abled person.
Communication is great with the property owner Sanja, she is keen that everything goes well on your stay. She even went above and beyond when I left my wallet in the apartment, and she kindly posted it onto me, making sure I received it promptly and safely.
Highly recommend, and would happily stay again.