In Spain you can take your bike on the local trains, or cercanías as they are called. On the longer routes they aren’t allowed so you’ll have to stick to pedaling. I found a bit of gear in my mountain climbing equipment that works very well to secure my bike on these short trips which beats standing with it the entire time. A carabiner attaches to the hand rail. Taking a local train with your bike allows you to see a lot more of the area than if you use Valencia as a starting and stopping point. Bon voyage!