Summary: Valencia is beautiful. The park in the middle of the city gives the perfect venue for a run, but I still took some time to run around in the old city centre, look at some old churches (Santa Catalina and La Seu de València are the two that I remember, but there were more), and enjoy the empty streets. Spanish people seldom go out at 6AM. I ended up doing another 10k here.
Weather: overcast 16°C, even rained a bit at some point; still enjoyable.
Fun fact: the city smells like an old city: mold and dog shit; but the city park makes up for the whole thing, with orange trees, and that mediterranean smell that you only get down South.