Most of what constitutes your address is in the Student Handbook, but here it is:
YOUR NAME
YOUR HALL & ROOM NUMBER (ex: Lora Robins C103)
Governor's School Program
28 Westhampton Way
University of Richmond, VA 23173
Your room number should appear on the letter from your RA. It's very important to include this information. And yes, the "University of Richmond" is the "city."
Since it's a long address and I write a fair number of letters and postcards, I like making up my own return address labels. Blank labels can be purchased from any office supply store, and you can just slip a page through your printer.
Naturally, anyone's allowed to write to you. Mail's delivered at least every weekday by 6:00. Remind them, too, that sending yummy snacks is also welcome.