if you're at Magic Kingdom, it's fairly easy to leave the park & hop the resort monorail which will take you the Contemporary (California Grill, The Wave, and Chef Mickey's) or The Polynesian ('Ohana, Kona Cafe, and the Luau), or the Grand Floridian (1900 Park Fare, Grand Floridian Cafe, Citrico's, Narcoosees) You can push the stroller right onto the monorail, no problem. When you're done eating, hop the monorail back to the park.
When you're at Epcot, besides being so many restaurants in the parks (including character meals) you can walk out of Epcot through the International Gateway (up in World Showcase just past England area) and walk over to the Beach Club (Cape May Cafe, Beaches & Cream), or Beach Club (Captain's Grill & Yachtsman's Steakhouse) as well as Boardwalk (Kouzzina, Espn Club, Big River Brewing, Flying Fish)
So from those two parks you can fairly easily get to a lot of additional restaurants without too much hassle.