I had a friend who stayed at a place called Hotel America or something like that on the main drag. It was most of the way down on the left. It was clean and had AC for about $25 a couple years ago. I know you say you don't need AC but in Granada it can be flat out miserable without it. This time of the year you really don't need reservations you will find rooms, don't worry about that, and in your price range the best thing to do is to show up and see what you like best. Have them drop you off in the plaza, walk down behind the big yellow church (honestly you simply can't miss it) and stop in several hotels until you find one you like. There will be almost a dozen renting rooms on that street alone, many in the $20-40 range. Go a block or 2 off that street and there are even more.