Welcome to AI.SE @Kate_Catelena!
I teach AI courses at the undergraduate level, and so have seen a lot of semester projects over the years. Here are some templates that often lead to exciting outcomes:
Pick a new board or card game, and write a program to play it. Your course has probably covered Adversarial Search, and may also have covered Monte Carlo Tree Search, or self-play reinforcement learning approaches. These projects are often fun to mark and creative because they are easy enough to be well done, and yet there are always new, exciting, domains to apply these algorithms to. Some examples of past projects that I thought were neat were an AI to play the boardgame Tac (mostly A* Search), and an AI to play the card game Love Letter (mostly Counter-factual minimax regret, the algorithm used to solve poker).
Pick a question that you would like to know the answer to, that could be addressed with machine learning. Then implement your own ML algorithm (decision tree learners are fairly easy), gather your own data, and show a result. Examples of interesting projects I've seen in the past are using ML to find out which of a number of factors most strongly influenced a students' subjective quality of sleep; and which items are most commonly purchased along with camping supplies (using association rule mining).
Anything involving reinforcement learning. RL projects are always neat to see if accompanied by a visualization showing the learner's behavior at different stages. A strong past project involved a student simply replicating Sutton & Barto's Acrobot experiments with their own implementation of the SARSA-Lambda algorithm. Other things that might be neat include making a trainable "pet" that the user can influence, or solving games using self-play.
Theoretical results might seem intimidating but are often more accessible than one might think, especially if your discrete math skills are strong. I have had many student projects where the student went away to look at theory papers in ML or Multiagent Systems, found a suggestion in the future work sections that wasn't a big result, but that was fairly easy to prove, and proved it. Sometimes these are even publishable.
Replications. Go find an interesting AI paper (use scholar.google.com), and then see if you can do exactly what the authors suggest and if you get the same result or not. Then, if you have time, see if you can improve on the results. These are often most interesting when you find a paper written in a different field that uses AI. Often the authors of such papers know less about AI than you do, and so it can be fairly easy to improve on their results. I have had several students do projects like this to great effect.
Those categories are a bit vague, but remember: AI touches almost anything. Pick your favorite hobby, and see whether you can relate it to AI using one of the approaches above. Nothing makes a project stand out like one that applies AI to solve some real issues in an exciting domain. Good luck!