I meant to write about it right away, but then got distracted by life 🙂 In short, public transportation turned out to be affordable and convenient. We took the subway from the airport to our hotel, then purchased multi-trip tickets and took the metro or a bus everywhere. The system is very similar to the one we have in Chicago, only you need to touch the card not only on your way inm but on the way out as well.
The only problem we faced was that during the evening hours, the time between trains during off-peak hours could be substantial: 20 minutes or more! The long wait was the only reason I took a cab or Uber: I did it three times.
Other than that – only positive things! I even tried to take a tram to the Valencia Postgres meetup, but then I’ve relaized how long it would take!