Being out of Wi-Fi for a few days, I was forced to go on a hunt for Wi-Fi enabled cafés to work from in central Valencia. You'll have no trouble finding cafés with Wi-Fi, but finding one with power outlets, and where they welcome laptops, is not as easy. I always ask up front if I can work with a laptop, so the ones I have listed here should be OK with that.
I've made this a community wiki, so feel free to add more cafés suitable for working.
A friendly café with amazing food and good music. Say Joaquín sent you ;)
Where: Los Maestres, 5 (in La Xerea, near Plaza de la Virgen and Carmen).
Hours: 10-19 (but doors open at 09)
Power: Only 2 outlets inside, by either entrance, and a couple outside.
Work environment: Great people running the place! Can be pretty quiet, but gets packed during mealtimes. And almost exclusively by local people. Music is from their own playlist, and I like it. They have a nice terrace out back too. Only drawback is that their seats aren't the best for working comfortably, but it's OK.
Menu: Really good! They change their lunch menu every day, and it's always delicious. Can't complain about the price either (€9.90), considering what you get.
It's actually a semi-fancy restaurant (upstairs), but with a lounge area next to the bar with very comfy sofas, plenty of power and a calm atmosphere. A great place to work without being distracted, and you're not distracting the restaurant guests either.
Where: San Vicente Mártir, 23 (between Plaza de la Reina and Plaza Ayuntamiento, across the street from Starbucks).
Hours: 12:00-00:30 (02:30 fridays and saturdays, for workaholics :P)
Power: Plenty of outlets in the lounge area.
Work enviroment: Comfy! Low coffee tables in the lounge, higher tables by the entrance. Good, quiet atmosphere to work in. Music is generic and low key, but gets old quick. Excellent service. (Do not use their restrooms though – did not love up to their image!)
Menu: Very good. You can order from the restaurant's menu, or try their own special crunchy tapas (€1.80), or coffee, drinks, etc. from the bar.
Café & Te (Plaza Ayuntamiento)
It's a big chain of cafés, but this particular place is more of a restaurant. It's possible to work from its two lounge areas, but beware – the staff won't necessarily like it when the restaurant fills up.
Where: Plaza Ayuntamiento, 8 (next to Burger King).
Power: In the two lounge areas.
Work environment: It's really a restaurant, but the two lounge areas (one larger near the entrance and a smaller further in) have comfy chairs and enough outlets. It's a lively restaurant in the evenings, so it can be a bit of an odd place to work, but it is possible. Don't overstay your welcome though, they will cut the Wi-Fi when the restaurant fills up to get rid of laptop wielding leeches. They could've just told me up front…
Menu: Extensive menu, being more of a restaurant (lots of tapas). Not bad, but definitely not cheap.
Café & Te (smaller franchises)
The chain's smaller cafés all have free, unlimited Wi-Fi. But nothing special.
Where: All over town.
Hours: No idea. Varies?
Power: You may get lucky, but don't expect to find outlets.
Work environment: Fairly standard cafés with mostly latino radio music. Decent seating and tables. Not the best work environment, but it might suffice if you just need Wi-Fi and a place to sit.
Menu: A fairly varied menu of hot and cold drinks, pastries, smoothies, etc.. At mealtime they serve hamburgers, pizza, salads, pasta, paella and more. Fairly standard, nothing special.
Not that suitable for working
Expensive "coffee", 40 minutes of Wi-Fi at a time, and can get packed with noisy tourists. So far there's a Starbucks at C/ Sant Vicent Màrtir 44, one at C/ de la Paz 44, and one at Gran Vía del Marqués del Turia 49. Expect one to pop up right behind you when you least expect it.
Subway, Burger King and McDonalds
Neither are good places to work (usually loud music and customers coming and going), but they do have free Wi-Fi. If all else fails?