Bluffton is a car-dependent town for most of its geography, but Old Town is genuinely walkable once you're there. The key is understanding the layout: Old Town sits on a bluff above the May River, connected to the rest of Bluffton by a handful of main roads.
US-278 is the main artery connecting Bluffton to Hilton Head Island and to I-95. Bluffton Parkway runs north-south through the newer parts of town. May River Road connects Old Town to the broader area. Once you've driven these three roads, you'll have your bearings.