Urbino is a university town and the bars around Piazza della Repubblica stay busy well into the night during term time. In summer, when the students leave, the city is much quieter. The main aperitivo run is along Via Veneto and Via Mazzini, where most places put out chairs onto the cobbles in the evening.
For coffee, the historic option is the Caffè Basili on the Piazza della Repubblica, in business since 1854 — perfect espresso, well-priced pastries, and a reliable place to read a book.