Upvote:1
After asking here and to a few locals, it turned out that a good option was Agia Pelagia (pics and map here )
It's really a nice place, very relaxing, with lots of choices for something to eat and a lounge beach bar at the west side.
It's at about ~20km away but it's maybe faster to go there by bus than to other closer beaches on foot.
There is a bus service for Agia Pealgia, that brings very close to the beach in a few minutes (usually starts at line 5 at the main bus station in Heraklion, ). The bus takes about 50 minutes to go, and around 30 to come back to Heraklion.
In the picture below you can find the bus timetable.