Well, Bloody Bridge is perhaps one thing worth visiting ( although there is no bridge there since 1898, I think ) - named after numerous conflicts during the centuries between Kaptol and Gradec, two separate boroughs.
Then, you could also visit the Upper Town, including Strossmayer's promenade, the astronomical observatory, Kamenita vrata and Kula Lotrscak ( 13th century) which is also a gallery, St. Mark's Square, with a gothic church of St. Mark in its centre, the cathedral...there are lots of places to visit there.
And if you are not that interested in history and museums ( and since you´re too early for Metallica´s concert in May ), check again http://www.zagreb-touristinfo.hr/?id=21&l=e
I am sure you´ll find something that suits your needs.