About 500 meters from the apartment - center of Okrug Gornji - there is a supermarket (Tommy), post office, bakery and a pharmacy (they speak English). When you came from the airport and had to find the apartment you turned right after the bumps if you had instead continued straight ahead you would have arrived to the center of Okrug Gornji.
It is not the same prices as we are accustomed to - it is cheaper, but the Croats have not as much money as we have - an average salary is around 3000 kuna a month.

The bread at the bakery is, as we know them - just much bigger - their danish are usually donuts or donuts look alike with different fillings. It costs almost nothing - and it is worth drive, run, walk or crawl after.
Vegetables can be bought from Tommy or any other supermarket, but if you are goiing to Trogir, we would definitely recommend the market in Trogir, located on the small island like you ran over to get to Ciovo, opposite the bus station - it is very very cheap and the quality is on top.
There are also all sorts of stalls where you can buy everything from cheap souvenirs to swimsuits and shoes. It is a nice and cozy place to zap around and feel the atmosphere and holiday mood.
Split is a great city to go shopping in, they have it all. Flagship stores with familiar brands, shops for those who will not spend so much money and markets, where you can make a good deal. Some of it is worthwhile to take home to Denmark are shoes. Shoes in Croatia are often Italian and although with Danish eyes are very cheap and of good quality. Pirelli is a great shoe shop exclusively with Italian shoes - it lies in Emezetta - a shopping center just before you come to Split.