Zagreb is pretty small, tourist-wise everything is basically a short walk from Jelevic Square. I would recommend staying around there. Hotel Jagerhorn is a nice choice. Zagreb has a lot of “quirky” museums you might call tourist traps in other cities, but seem to suit the youthful college vibe around here. The Museum of Broken Relationships and the Museum of Naive Art are legit top-notch museums. Don’t miss them. I would also recommend finding yourself a guide for a good walking tour for some Croatian history and hidden spots.
I find Zagreb to be just a very friendly, charming city. It’s a perfect place to chill. It rewards exploring, there’s a lot of little passages and courtyards tucked away. Summer is happening, with tons of people out enjoying themselves every night of the week. On separate trips I found a big free music festival in one of the big parks, and a local food truck/party zone behind the National Theatre. Great fun. Be sure to treat yourself to some ice cream, some of the best anywhere.