There are plenty of places to visit and activities to enjoy in knoxville, TN area that are appropriate for dates and require very little or no money, assuming that you will only need to pay for gasoline or transportation.
1.) Grab the frisbee and pick up your date for a fun afternoon or romantic evening in one of the many parks throughout the Knoxville area. Some of the nicer parks include Lakeshore Park in West Knoxville, Victor Ashe Park in Northwest Knoxville located near Northwest Middle School, Northshore Park located on the waterfront off Northshore Drive in Farragut, Ijam's Nature Center in South Knoxville, and Forks of the River WMA located in East Knoxville.
2.) In warm weather, you can enjoy swimming at the Cove (a manmade beach) located inside Northshore Park of Farragut. You will also find a playground, beautiful walkways, volleyball nets, and plenty of places to picnic, relax, and have a great time. You might consider inviting a group of friends to go along on your date and take a volleyball, baseball equipment, or maybe tennis gear to enjoy a match on one of their many courts.
3.) You can also take advantage of the fact that you are only about 45 minutes from the famous Smoky Mountains National Park. You can easily plan an entire month of dates just in the Cade's Cove area alone. There's the Chimney's Picnic area where you can enjoy a meal by the river and hike the Chimney's Trail. Then there's the 5 mile round-trip hike to Abram's Falls and the shorter trail to Elijah Oliver Cabins that starts just next the trailhead to the falls. You will also find a very interesting old grist mill that is still operational in the cove and plenty of other interesting attractions.
4.) Another great place to go on a date when you have little money is to visit the Gatlinburg Visitor's Center and catch the trolley car that will take you around Gatlinburg. There are always plenty of bright lights and interesting sights along the main strip. I have fun just people watching and enjoying the sights and sounds of the area. At the very last red light in Gatlinburg you can walk behind the Burning Bush Restaurant building and discover a very nice walking trail that follows the river and has canopy of tree branches that shade the entire pathway.
5.) You might also enjoy Market Square in downtown Knoxville. There are plenty of trendy shops there and in winter you can people watch at the outdoor ice skating rink.
6.) Another fun activity is to go to the Fountain City Duck Pond. Don't forget to take some bread or stale crackers to feed the ducks.
7.) Of course, if you don't have money or transportation, then you should consider inviting a group of friends over. Tell each person to bring their favorite board game, and a beverage and snack item to share. Some of my most memorable dates involved board games and loud, roudy friends.
8.) Gather a group of friends, collect a few dollars from each, and pitch some tents at the Mountaineer Campground in Townsend. It isn't far from Knoxville and the campground has a swimming pool and there is an arcade next door. Be sure to look up some spooky ghost stories to laugh over by the campfire. Marshmallows and hotdogs are always a good idea too.
9.) You might even consider staying home and watching a movie or taking a walk at West Town Mall.
If you want to come up with more ideas, then go to the Knoxville Chamber of Commerce website and see what is posted on the current events and activities calendar. There are always fun things going on around the city and many are free.