If I think about all of the dining rooms of all the Airbnb's we've stayed in, there's a flash of many memories. Eating, working, playing games all around various tables in various cities with our family or our friends. Sometimes at really creaky unstable tables, sometimes on uncomfortable chairs, and sometimes, I'll call them the best times, we sat around in a nicely designed dining area with chic and quality furniture.
The dining table and chairs are the work horses of your rental, like the sofa. You don't want to go super cheap with these items because it will get a LOT of use and abuse over time. Stick with quality and durability.
Don't have space for a formal dining area in your rental? Not to worry! A little eating nook or bistro set will be great. What matters is that you offer some kind eating space for your guests, and bonus points for you for thinking about the design of that area to make your rental stand out.