Yellowstone PlannerThis will get you started. Also from here search the park website for day hikes in YELL. Over a thousand miles of trails...HOWEVER the first thing that you will note is DO NOT hike alone in the backcountry. Hike in groups of three or more. Carry and know how to use bear spray. Overnights require a plan, and a permit.
It is grizzly country, and there have been many incidents over the years. True bushwhacking is not encouraged because thin crust areas where you can be severely burned can and do occur anywhere in the park.
Very few trails are loops, most are in/out from the roadside.
Be prepared and be careful, have a plan for bad/freezing weather and communication i.e. SPOT. Cell phone coverage is still non existent except village areas.