Unofficial trails on Mt. Philo are described here!
The Blue Gate Trail: It's easier to begin at the top and walk down, as the section through the field is steep. Start at the large blue gate. This can be found halfway up on the north side of the north access road (down). Pass through the blue gate, which is locked but passable by foot. Follow the trail North into the field. Take a look around, because these are the best northern views of Lake Champlain. Follow the trail down the wide grassy slope bearing northwest. You will soon reach a newly re-graded, though unused road. Follow the new road till you reach the base of the hill. Pass the pond on your left, then circle left (south) along the mown trail through the field till you reach the west side of the State Park parking lot near the entrance. 2.5 - 3 miles, mild-moderate difficulty. Thank you, ranger Nate Goddard, for keeping this mowed and accessible. View from the Blue gate trail
Best northern views of the Champlain valley!

Trail View
The view north from the main trail. Photo by Adam White.  A lovely stop, near the top  Mt. Philo road in 1924
Undated postcard from the Mt. Philo Inn near the top of "one way".

Trails
Mt. Philo has a variety of wonderful hiking trails leading to picturesque vistas, lovely settings, and unusual land formations. Most visitors walk along the road, which is a one way traffic loop for the top section. It has occasional slow moving auto traffic, and infrequent bicyclists, but is wide and safe. A trail leads from the lower parking area to the top, crossing the road about half-way up. The trailhead is found just behind the information booth. The youth conservation corps have done an excellent job in recent years improving accessibility and keeping the trail safe in wet weather
A trail map of Mt. Philo State Park
An official PDF map from the state of Vermont of trails can be found
here trail map
This nice mash-up from Local Motion shows the trails and restrooms in relation to a USGA satellite image ttrail map
good work by YCC
The Youth Conservation group has done a wonderful job making the trails accessible and crafted.
New Trail Update (9/23/11) The youth Conservation Crew has recently completed work on the top section of the lower trail where it intersects the road. When coming up hikers should now go right instead of left at the road

Running
Many runners inhabit Mt. Philo, including ultramarathoner Joe Carrara, pictured below, and Vermont champion Jack Pilla.
Run the trails, do some reps up Philo, or try ask the innkeeper for more information Joe Carrara