The drive from Harrison to Ponca on Arkansas 43 (through Compton) offers many grand vistas of the Buffalo River Valley. Be sure to do it in the afternoon, so that the sun is to the south or it's even nicer later when the sun is in the southwest. In fall that's earlier (3-5 pm). In summer that may be as late as 6-9 pm. You need to be very careful as the road is only 2 lanes and there are no 'official' places to pull over.
If you want to stop, find an open streatch with a view and a drive or side road.
The entire 135-mile length of the Buffalo National River is well off the beaten path. There are no gateway communities such as exist at the entrances to many national parks, and there are no towns along the shores of the river.
I purchased a postcard for Karen at the Tyler Bend Visitor Center, but was told by a park ranger that they had no mail drop for visitors there. He directed me about 3 or 4 miles north along US-65 to the rural village of Saint Joe (pop. 85), where there is a U.S. Post Office on the west side of the highway. In addition to the Post Office, there is little else in Saint Joe except a new school building and an old general store (see photos).