Do you have plenty of light? Most edible plants require at least six hours of sunlight daily. Not sure what a tower garden is specifically, but vertical gardening strategies would work in a sunny window space, along with herbs and such on windowsills.
Greens and herbs can be done in small containers. Maybe strawberries, and cherry tomatoes in a hanging bag or pot. I suppose you could grow carrots, radishes and some other smaller root vegatables in smaller containers. If you have enough light (or want to get into hydroponics and indoor lighting systems.)