The biggest and best known market in Zagreb is the market Dolac that you can find just couple of meters north from main square of Ban Jelačić.
In the late 19. century the main market was organized on the main square but as the city grow it was needed more space so the market was moved to the todays place. This the most famous farmers` market of Zagreb is busy through the week. The best time to visit (when it is most crowded) is before noon. So if you want fresh fruit of vegetables this is the place you have to visit. Make sure to take your camera because you will like red umbrellas that are covering numeros stalls. In the northern part you will find flower market and stalls with clothes.
A fish market can be found in the north-west corner. In small bistros and restaurants aside of the fish market you can eat fresh fish or squids (for a fair price).
There is also a lower and covered market where you can buy meat and local speciality cheese and cream (ask for “sir i vrhnje”).
Generally, travellers like this place, not just because of fresh food but because it shows real life of Zagreb in its center, overlooked by Zagrebs cathedral.
After shopping, go to the Tkalčićeva street or Cvjetni square for a nice cup of coffee (there are plenty of cafes that you can enjoy) or if you want more relaxed atmosphere, buy a coffee to go and head down to Zrinjevac and relax on the grass.