Zagreb, capital city of the Republic of Croatia since independence in 1991, is an old-style central European city. For centuries a focal point of culture and science, it now has international pretensions and seeks to exploit its position at the intersection of important routes between the Adriatic coast and Central Europe. It's the country's political and administrative centre and hub of the business, academic, cultural, artistic and sporting worlds in Croatia.
More than that, it's simply lovely - a thriving smorgasbord of Baroque atmosphere, picturesque open-air markets, diverse shopping opportunities including an abundant selection of crafts and picturesque fruit and vegetable markets, many green parks and open spaces for walking.
In spite of the recent rapid economic development and improved transportation infrastructure, it retains its charm along with a relaxed feeling that makes it a human city. All this, plus 10 theatres, 21 museums, 14 galleries, and 12 permanent art collections.
Quick Tips:
To get a feeling for both historic and modern Zagreb, wander through the streets of the Lower and Upper Towns plus the grander museums and administrative buildings - each has a quite different feel.
The Upper Town (comprising Kaptol and Gradec) with famous St. Mark's Church (its painted roof appears on every postcard and it's virtually a symbol of Zagreb), the best city views from the landmark white Lotrscak Tower and Zagreb's cathedral and markets (like Dolac, east of the cathedral); the Lower with a multitude of art, history, and sculpture, plus some glorious Austro-Hungarian buildings on the walk from the station to the main square.
I also found it worth understanding a bit of the history of the place, both to appreciate the architecture in context and the inordinate amount of statues of writers, politians, historians, artists which are virtually around every corner and whose place in the grand scheme you won't know without some grasp of how the history fits together.
Best Way To Get Around:
Despite being on two levels, the centre of town is nonetheless pretty compact - cheap, regular trams run all round if you should want to venture outside the main drag and the only other form of transport you're likely to use is the KN3 funicular (which runs every 15 minutes or so and takes all of 30 seconds - it might be worthwhile if you've had it with hills or are in a hurry to get to the Upper Town for example for the noon cannon) and drops you right outside the Tower.
A Zagreb Card costing KN60 (about US) is valid for three days/72 hrs and will get you a 50% discount off entry into the museums/galleries and free transportation/50% off city bus tours (which I don't think are worthwhile - this is a place for mooching and enjoying whatever is round the next corner.