The reason I would say to stay inside the city walls is that you don't have to drive around as you're close to the nightlife. Otherwise, you have to look into renting a car or public transport.
I can suggest the Albergo La Perla
hotel which is located in Indipendenza Square near 'Piazza del Campo'. The rooms are small but clean and rates start at $44 but do check with them before booking.