For a 'walking' gun, I stick to the Ruger 77/22 vhz Hornet. I avoid the 22-250's and 243's in a 'walking' gun, because I woun't be taking shots out past about 200 yds with it. For the long range shooting from a rest, I'll use a heavier and more expensive gun - both negative attributes for a walking gun that gets carried and banged around a lot.
I also have a rem 788 in 222 that I think would probably make a devent walking gun, except for the lack of sling studs (which is an oversight that will soon be corrected.)