My idea is to have the letter "I" in YRIT be single column from an academic building (see the attached image for an example). You Reach I Teach is also a play on words, stemming from the "crossover" dribble in basketball. In terms of imagery, I'd be interested in seeing a basketball player performing a crossover dribble, with an academic hat on his head. With my interest in getting into apparel with this logo, I could see that image being used as a stand-alone sometime (similar to the Jordan Jumpman logo). I've attached a few image examples of the crossover dribble.
In sequence, I picture (left to right): Basketball player, YRIT (with You Reach I Teach directly below it). I'd be open to seeing designs with this laid out differently. Feel free to use your creative flow to add new touches.
Modern typography is important for me. I want this to be a logo that those in basketball culture and outside of it can appreciate and can take seriously. I also want this to be something that could be appealing on basketball shorts, socks, tees, etc. Clean, sharp, professional, fun, empowering. Nothing cheesy.
Colors: I'm picturing the basketball player in black or gray, the basketball in orange, the YRIT lettering in black or orange, and "You Reach I Teach" in a powder (Carolina?) blue. I'd be fine with seeing these colors mixed some, depending on what the designer feels looks best. These are just suggestions.