Because KiryÅ« was largely unscathed by World War II bombing, it contains one of the highest concentrations of prewar urban architecture in Japan: wooden-sided warehouses, sawtooth-roofed textile mills, merchant stronghouses, and Meiji-era adaptations of Western buildings. The old urban core of the city is easily walkable. Here's one suggested footpath through a living—indeed, bustling—architectural museum (http://homepage1.nifty.co...).
From the North Exit of JR KiryÅ« station, swing to the right around the plaza and look for Fuji Halal Foods on the corner of Yamate-dori, running north, and Suehiro-dori, a major east-west thoroughfare lined with shops of all kinds. Walk up Yamate-dori past the modest Nishi KiryÅ« terminus of the JÅmÅ commuter line. Yamate-dori will drift toward the right as it hugs the base of the hillside to its left.
When you see the entrance to Nishinomiya shrine with old stone steps from the sidewalk down to the street, turn right and walk east to Honcho-dori, Kiryū's major north-south thoroughfare and where Prefectural Route 66 passes through the city. You'll be at the boundary of Honcho 1-chome to the north and 2-chome to the south, with a branch of Mitsukoshi on your right, and a gentrified cluster of former warehouses Yūrinkan to your left across the street. If time and interest permit, take a walk through the art and craft galleries inside.
Then go straight up Honcho-dori for a few blocks before turning right and coming back down Nakacho-dori, which is roughly parallel to Honcho-dori but drifts east. Look down side streets for interesting architecture as you go. Be sure to stop at the textile museum Yukari across the street from Kiryū Catholic Church down a side street on the left a few blocks north of Suehiro-dori.
When you get back down to Suehiro-dori, turn right to head back to JR Kiryū station. There are many choices along Suehiro-dori of places to reward yourself with food and/or drink after the walk.