Some examples of assignments that people have completed include photographing objects that are a particular color or shape. Your subject might be a theme involving the use of reflections (as in glass windows or puddles of water), or texture (light raking rough surfaces in the early morning or late afternoon). If you're the outgoing type, some photographers make a project of photographing strangers - either as candid street photography or directly asking people to stop and take their portrait. Lousy weather? How about some macro photography on the kitchen table? Ask your friends if they'd be willing to model for you, and practice lighting techniques with a lamp and a $1 white foam board. These are just a few ideas, but you may be able to think of many more on your own that suit your interests and personality. If you're looking for more ideas, take a look here or here.
If you can't think of a specific project idea that appeals to you, a related idea is to seek out festivals and events in your area via Google. Most communities have some version of an events calendar online. In east Tennessee, the best time of year for festivals is typically summer and fall. Grab a favorite camera with a single lens (more lenses will just slow you down), and head out to photograph the festivities. Your local farmers' market is packed with people, produce and other goods. If there's a "Zombie Walk" or comic book convention in your area, you'll have no trouble getting spontaneous photos as participants are usually eager to show off their costumes.
I work these events as if I were on a paid job assignment, and people sometimes assume I am. Whatever assignment you decide upon, tackle your project as though you're a staff photographer for a newspaper. Just because you're not working for pay doesn't mean your assignment is any less important. Look at every detail as something that others might not see apart from your efforts to document it. Things you normally take for granted as boring fixtures that "everyone" has seen aren't boring to someone on the other side of the globe or across the country. You might be surprised at how the world around you looks from the fresh outlook that an assignment provides.