Need internet, a book or info? Backpacker's C@fe!
It's near the Post Office, at the beginning of the quey side road that leads to the ferries.
Kneza Domagoja Obala.
I found a very kind and English speaking person that helped me as well as giving me an espresso and water at 5 kn (elsewhere 7 kn, if walk far enough from the Riva you can get it at 4 kn).
The place is not only a cafe but has second hand books in many languages and internet. If you buy a book you get some internet time for free.

Basement of Diocletian Palace
Bell tower of St. John church
Dome of Kris church on horizon
Looking up to tower