Its not a Shengen area but you can still enter just with a passport.

Green and architectural. Zagreb is a city with lots of greenery even right in the city centre. One prong of the so-called green horseshoe stretches from Zagreb Railway Station  to almost Old town past the Trg Kralji Tomislava, the art pavillion, the Trg JJ Strossmayera to the Trg Nikole Subica Zrinskog. Near the railway station there is a statue of King Tomislava sitting on his horse. The art pavillion is a very attractive bright yellow building. This area also has statues and fountains. There are plenty of seats here to relax on in the shade. Both sides of this green area are lined with beautiful buildings with ornate facades.

Upper town or Gornji grad is full of history. It’s a 15 min walk from station. Stat your tour with Entering old town from narrow path to Lotršćak tower (fortified tower from 13th c.) on the left side of main squire, and enjoy in panoramic view from top, then go to the famous St. Marks square with St.Mark;s colorful rooftop church, then go trough Stone gate (the eastern gate to medieval Gradec Town, now a shrine. According to legend, a great fire in 1731 destroyed every part of the wooden gate except for the painting of the Virgin and Child (by an unknown 17th-century artist). People believe that the painting possesses magical powers and come regularly to pray, light candles and leave flowers. Square stone slabs are engraved with thanks and praise to the Virgin.) and follow through popular Tkalča street (pedestrian narrow street with little stores and boutiques) to Cathedral of Zagreb on Kaptol that is a Roman Catholic institution and not only the tallest building in Croatia, but also the most monumental sacral building in Gothic style southeast of the Alps. Then return to the Ban Jelačić square which is the main square in the city.

The Zagreb Cathedral on Kaptol is a Roman Catholic institution and not only the tallest building in Croatia, but also the most monumental sacral building in Gothic style southeast of the Alps