Personally don't like dealing with the lines coming in from West every day. One buffalo jam and there goes your morning. Have you checked out Flagg Ranch between YNP and GTNP? Never stayed there but getting in and out of both parks convenient from there. One can also stay in GTNP but more of a drive each day. These options aren't as close as West to Norris and Old Faithful, but they are closer for the east side attractions such as Canyon, West Thumb, and Lake. Maybe spilt up your stay between West and somewhere to the south?