Yellowstone National Park offers 97 trails totalling 957 miles! This vast array of trails offers visitors an excellent chance of solitude and scenery. Yellowstone National Park management advises that you visit the local ranger station before setting out on any hike so you have have the latest information and permits.

A few day hikes:

Avalanche Peak: 5 miles round trip (west end of Eleanor Lake)
Elephant Back Mountain: 3 miles round trip ( 1 mile south of Fishing Bridge Junction)
Howard Eaton: 7 miles round trip ( parking lot on east side of Fishing Bridge)
Natural Bridge Trail: 3 miles round trip ( Bridge Bay Marina parking lot)
Pelican Creek: 1 mile round trip ( 1 mile east of Fishing Bridge visitor center)
Pelican Valley: 6 miles round trip ( 3 miles east of Fishing Bridge visitor center on dirt road)
Storm Point: 2 miles round trip ( 3 miles east of Fishing Bridge visitor center)
Cascade Lake: 4.5 miles round trip ( 1.5 miles north of Canyon Junction on Tower Road)
Grebe Lake: 6 miles round trip (3.5 miles west of Canyon Junction on Norris road)
Purple Mountain: 6 miles round trip ( 1/4 mile north of Madison Junction)
Two Ribbons: 1.5 miles round trip ( 5 miles east of West Entrance)
Osprey Falls: 8 miles round trip ( 5 miles south of Mammoth on Bunsen Peak trail)
Wraith Falls: 1 mile round trip ( 1/4 mile east of Lava Creek Picnic Area)
Grizzly Lake: 4 miles round trip ( 1 mile south of Beaver Lake on Norris Road)
Artist Paint Pots: 1 mile round trip ( 4.5 miles south of Norris on the Madison Road)
Monument Geyser Basin: 2 miles round trip ( 5 miles south of Norris Junction on the Madison Road)
Lone Star Geyser Trail: 5 miles round trip ( 3.5 miles southeast of Old Faithful area)
Mystic Falls : 2.4 miles round trip ( Biscuit Basin Boardwalk)
Yellowstone River Picnic Area: 3.7 miles round trip ( 1.25 NE of Tower Junction on Cooke City Road)
Slough Creek: 2 miles round trip ( near bathroom at end of Slough Creek campground)
Shoshone Lake: 6 miles round trip ( 8.8 miles west of West Thumb Junction)
Duck Lake: 1 mile round trip (West Thumb Geyser Basin parking area)

Equipment checklist:

Sturdy and lightweight tent
Comfortable backpack
enough water for your hike or a quality water purifier/filter
raingear
a sleeping bag rated properly for the time of the year
comfortable, already broken in hiking boots to avoid blisters
matches or lighter
hat and gloves in crisp conditions
quality winbreaker and liner
proper amount of food (high odor items are probably not a good choice)
sunblock
a hat
sunglasses
camera
bear spray
cooking utensils
knife
scrub pad
20 feet of light rope
insect repellent
sleeping bag
cooking stove