I don't drink much soda or alcohol. Is plain water readily available?
Yes, water is readily available at any bar and at the non-alcoholic beverage sections of all food service areas.
Don't bother with bottled water aboard ship. The regular tap water comes from the ocean via a distilling plant. It's far more pure than most water ashore, including what gets bottled for sale in your grocery store back home.
the tap water is very good. What we do is to purchase the sports bottle size of water in port at the grocery store before we board the ship. Then we will refill those bottles as needed from the tap. Just note that the tap water isn't very cold, so fill your water and put it in your stateroom's fridge.