I'm not aware of a map that shows stroller parking. But the areas are ubiquitous and readily apparent. You will either see a stroller parking sign adjacent to an attraction, or a veritable parking lot of strollers already parked.
The country pavilions in Epcot comprise both indoor and outdoor areas. The indoor areas might consist of an attraction, shops or restaurants. Just like anywhere else in the parks, strollers are not allowed inside attractions, and this includes queues and preshow areas( strollers tagged for use as a wheelchair are excepted). Generally strollers are not allowed inside restaurants.
You have to remember that there could be upwards if 50,000 people in Epcot on a busy day. Allowing strollers inside would quickly result in gridlock.
If your child needs a nap, there are plenty of shaded, quieter areas outside where you could spend some time. You can get in a quick nap (in airconditioned comfort) in the comfy seats of American Adventure. The France movie is only 18 min, but the seats are really comfy, too. And the music is very relaxing.