Our plan for Cinque Terre (my birthday!) is pretty much the same! So looking forward to a day centered around food, drink, a little swimming, and soaking up the villages and photo ops. I too want to try a little bit of a hike so I think I'll take your advice for that short Lovers Walk and use the Cinque Terre Train card pass for the rest of the day.
I have usually bought bottled water on the cruises leaving from Florida because we have time to pick some up at a supermarket or drive down and bring some from home. I never really thought about it, but the water on the ship is great. Its filtered and great quality. I just always like having a bottle for excursions and gym time. Now, you can bring a bottle and fill it up at the drink station, BUT you cannot fill your bottle directly from the spout because of germ concerns. You have to use their tiny cups and fill your own cup with that, which gets time consuming. But I had the same thoughts as you for the med cruise- wont be as easy to get bottled water and certainly not as cheap as at home. So I asked my trusted TA if the water in the sink in the room is the same as at the drink station, and she said it is exactly the same, and she uses it often to fill her bottles for water. So that is what we are going to do. Will save us money and space/weight in luggage, and we'll bring our own bottles and easily fill them from our sink and have a couple chilling in the beverage cooler at all times. Seems like the best way to go.