Downtown Knoxville is a charming area to explore and you'll find a mix of historical buildings and modern businesses. If you're looking for a bite to eat, many restaurants and cafes welcome pets, usually on the patio outdoors. If you plan on doing this, check the weather, especially because the winter in this area can bring freezing temperatures.
Downtown Knoxville is essentially the center of the city, meaning that it's the most crowded with cars, bikes, and people. With heavier traffic, it's important to keep your pet on a tighter leash on the sidewalks and look both ways before crossing the street. Avoid walking near the ramps to the major highways and you'll be sure to have an enjoyable time in the neighborhood.
If you head south by the riverside, you can hop on one of the city's greenways which will take you on an adventure down miles and miles of trails that follow the Tennessee River. Pets are, of course, allowed on the greenways, but must be kept on a leash at all times.