Just a 5 minute walk east of the mosque in a residential neighborhood, on an incredibly narrow street, with about 5 prized private parking places. The door is always answered by a mature, friendly adult. I was unsure about staying in a place with "hostal" in the name, which conjured up images of bunk beds, and odd teenagers running the place -- This was nothing like that! The managers seemed to me to be a family of brothers and sisters around 60 years old. At checkin, they took the keys to my car, and kept it safely parked out front for free, moving it whenever they needed to. They offered advice for locally favorite restaurants that proved very accurate. Travelers speaking only English may not be able to enjoy this benefit to the full, however, as most staff I spoke to seemed far more at ease with Spanish.
Hostal Osio was a bargain for 45 Euros nightly. The room was perfectly clean. It's an old family home, generously decorated with plants and colorful furnishings. There is a small "internet room" where you can go online with the desktop provided (for a nominal fee), and there is also a hot coffee/tea machine.
My wife and I visited Cordoba for 4-days in mid-December, which is very off-season, but we were lucky to enjoy terrific weather: sunny, highs of 68 degrees, but chilly lows in the 40s. Throughout the south of Spain, heating is used sparingly, but Hostal Osio cranks it up from about 8 p.m. until 2 a.m. which sends you nicely off to sleep, but getting out of bed in the morning can be an eye-opening experience. Obviously this a purely a seasonal consideration and not a concern in the baking-hot summer.