There is but one table service restaurant at Port Orleans Riverside.
Boatwrights Dining Hall is a shipyard-themed casual restaurant located just off the main lobby. We ate breakfast there a couple of years ago and found our meals to be plentiful and yummy. They've made a few changes in that they now only serve dinner, but it is a very convenient option if you want a hearty meal close by. Of course, the food court on site also offers a wide variety of tasty fare, just in more of a fast-food type setting.
If you have some time to spare, Downtown Disney is easily accessible via the boat launch from the Port Orleans Riverside marina. The boat ride takes roughly thirty minutes, give or take, but it's a very pleasant and relaxing trip down the water. Once you arrive at Downtown Disney you'll find a ton of dining options including table service and counter service. My family is especially partial to Wolfgang Puck Express and Earl of Sandwich. Both are counter service locations though the quality of food you get for the money puts fast food joints to shame. The menu at Wolfgang Puck Express offers a little of everything; even the choosiest of eaters will find something to enjoy there. You could also try Rainforest Cafe or the new(ish)
T-Rex restaurant. And don't leave Downtown Disney without stopping at the Ghirardelli Soda Fountain and Chocolate Shop for one of the most heavenly sundaes you've ever tried.
Enjoy your stay at Port Orleans Riverside; its my favorite moderate resort!