I'm staying in Rimini and could make the trip to Urbino starting anytime after 1:00 in the afternoon on a weekday. Should I do it? What is there to see/do, and would the trip be an okay length to get there and back at a reasonable time?
It's over one hour, if you drive. Search on Google (including Images) and see if you might be interested.
Otherwise, closer to Rimini, there is also San Marino that is nice to visit. The Gradara castle is nice too. And from Rimini all the way to Gabicce to the south there is plenty of beach scene too, if you prefer.
Urbino is definetly worth seeing. I spent most of a day and wish I had had more time. I'd try to make it out before 1 if possible.