The Washougal River Greenway Trail is a great place to take a walk through natural landscape, along the river, and explore a little. The two ends of the Greenway Trail are at NE 3rd Loop and at Beaver Park. Both areas have space for parking, though more at the Beaver Park end.
From the NE 3rd Loop trail head, you could walk a short distance northwest, across 3rd Ave, and start up the Lacamas Creek Trail. Along the Greenway trail, there are several unpaved side trails that can take you either to the river, and around the ponds. At the Beaver Park end, you could continue on to Goot Park (also where the nearest public restrooms are located) and loop back across the fields under the power lines to reconnect from side trails.
The other side of the Washougal River has another area of trails to explore along the Washougal River Greenway.