If you're talking about spring /summer, Harriet Lake might be a nice camping spot away from 224. It's a bit under halfway to Timothy Lake just off Road57 . A couple other little forest service roads from just past there would take you to Hideaway Lake (and the beginning of an access to Shellrock Lake and the Rock Lakes Trail) . For novice hiking Timothy Lake might be better. It's basically a flat 12 mile loop that you can do all or part of and pretty much have no fear of getting lost.
If you are talking about going now in winter, the road connecting 224 and 26 (FS Road 57) is snow covered and closed. The Forest Service does not plow their roads, it will not open until the snow melts. The USFS Mt Hood website updates conditons every week or two..