Burren National Park encompasses quite a sizeable area. Some parts are more recognizable than others, but you may not realize you're there from the surrounding scenery. On N67 you are indeed in the Burren, so it depends on what you really want to see.
I think of the heart of the Burren as the area where the Poulnabrone Dolmen - one of the key, if not the key, attractions - is located. There are a few interpretative signs describing the history, geology, flora and fauna of the park as you walk from the parking lot to the Poulnabrone.
To get there from Ennis head north on R476 to R480. You'll see signs and the parking lot on your right a few miles south of Ballyvaughan. It's a popular stop, but I've never seen it anywhere near crowded.