08/17/2010 AT 10:00 AM EDT
Did she work up an appetite? Rumer Willis
, dressed casually in a Market T-shirt, headed out to lunch with a pal at Urth Caffe in West Hollywood – then enjoyed a walk in Runyon Canyon
with Ashton Kutcher
and their dogs. At lunch, the starlet was in "chipper spirits," an onlooker says.