P.M.
Probably the only "rule" for art in the dining room is to choose something that won't ruin appetites, for family or guests. Seasonal pictures work all year if you enjoy them. It can be pleasant to contemplate another season when you've been suffering from summer heat or winter cold for awhile.
Another idea is to hang nature on your walls. Hang a dried wreath or even a fascinating piece of driftwood on your walls, place 3 or 4 smaller shadow-box frames side by side with lovely objects like leaves, grasses, feathers, seashells…. Nature never goes out of style.
Kids art can be adorable. There are frames with fronts that open so you can switch out drawings easily. These frames also work for framing your own selection of images that please you, from photos to magazine covers. I've occasionally framed swatches of gorgeous fabric or designer gift wrap with an inspiring quote or small photo mounted on it. The effect can be both stunning and highly personal.
What pleases you (and your family) is the most important factor when choosing art. Don't worry about trying to impress guests. You could end up with something "safe" but boring. You'll be looking at what you hang every day. Don't be afraid to experiment with low-cost approaches. You'll eventually discover what speaks to you the most.