The fridge in the Inn rooms is the same size as the fridge in a regular studio. So just under the counter height and with a small freezer at the top.
Last trip to Vero, we fit the following in the freezer - a 750ml bottle of vodka, 3 water bottles and 3 small round rubbermaid containers that we used to make blocks of ice for the cooler bag.
As far as the fridge, I've fit a whole watermelon, though usually I cut up the watermelon and put it in tupperware before putting it in the fridge. I've fit a couple 12 packs of canned beverages, multiple medium-large size tupperware containers, a dozen eggs, a bag of grapes, 4 ears of corn, cold cuts, cheese and various other food items stored in ziploc bags/containers. So, while not huge, if you're organized, you can fit quite a bit in the fridge and freezer.