Zagreb is a delightful city. Small enough to see most of everything on foot, although if you need it, the tram system seems very efficient and not too hard to navigate.
get a brochure, explore the market and then do a bit of a walking tour of Zagreb.
The only thing that was confusing was the way the streets are named and referred to. Essentially, there's a formal name like "the street of George Washington" but then some signs say "Washington's Street." But the way they do their possessives it can look even more confusing.
We spend a good deal of time following the suggested walking tour, first of the older upper town (Gornji Grad) and then of the newer lower town (Donji Grad). Upper town was originally two towns/settlements--Gradec and Kaptol--separated by a river. The river is now a street but the town names remain as neighborhoods within Zagreb. There is an old town gate that separated the two once upon a time. Much of Gornji Grad is primarily zoned for pedestrians (although service/delivery vehicles and scooters/motorcycles are allowed). Tkalciceva is the most popular hang out street in Zagreb. It's wonderful--adorable and filled with cafes and bars and great people watching.
In lower town we walked around the "green horseshoe." This is an urban planning project that added some lovely green space to Donji Grad and on a map is sort of shaped like a horseshoe. It includes the park around the National Theater/Tito Square and the Botanical gardens.
Mirogoj Cemetery: the cemetery includes a series of arcades and even outside of these, there is a great deal of tree coverage so it wasn't unpleasant to walk around. This is a beautiful cemetery.
Diocletian's Palace is something that must be seen to be believed. A medieval town built up inside and around a Roman Emperor's Palace. The entire thing is amazing. I've heard some have suggested that the city be emptied out and the entire place should become (essentially) a museum. Heresy! The fact that there is LIFE going on in this amazing structure is part of what makes it so fantastic