I could recommend hotel Alma Domus, one of the cheapest
hotels in Siena.I am pretty sure that the cost will be less than 80€ per double room as you asked. It is not very close to the city centre but just around the corner from the church of San Domenico. I heard the services are good and the rooms are convenient but not too big, so why don't to call them on +39- 0577 44177 and make your reservation..