Luckily I live near the KATY Trail which is an excellent trail to run, bike or walk on. I primarily run on the trail throughout the year (just passed my 3,000th mile running).
Background
The KATY Trail is a Missouri State Park. The trail runs along the former Missouri, Kansas, and Texas Railroad right-of-way in close proximity to the Missouri River (at least in my area). The trail primarily runs in the East-West direction across the State of Missouri for 240 miles.
A Wikipedia article gives further background on the KATY Trail.
Excellent Features of the Trail
1. No cars or road traffic to deal with.
2. Next to the Missouri River, so it’s cooler to run on during the summer.
3. Trail runs through woods and open fields. Can pick type of area you want to run through on a particular day. On sunny, hot day can run in woods. On overcast day can run in open areas.
4. Crushed limestone surface is easier to run on then asphalt or concrete. Less strain on your legs. Suitable for most types of bike tires.
5. Nice atmosphere. In short amount of time can be running through the middle of the woods.
6. Wildlife is prevalent. Often see deer, rabbits, squirrels, ground hogs, skunks, and hawks. Have even seen owls and eagles.
7. Trail is very flat since it is based on a railroad right-of-way.
8. Trail is kept up very well since it is a Missouri State Park. Many access points and parking lots along it. Some bathrooms.
Usual Starting Location for running on the Katy Trail
Access Point at Page Ave Extension Bridge (New Bridge) crossing the Missouri River.
I highly recommend the KATY Trail!
John Dorsey IT Brigade Inc. 
