If you're looking for a budget accommodation in the Medina, by all means check out the Hotel Sherazade. It's located in a small side street and is quiet, clean and absolutely beautiful. The Moroccan-German management is very competent and friendly, the breakfast served on the roof terrace is superb.
Prices are from MAD 180 per room and night (that's about EUR 16!); be sure to make a reservation since it quickly fills up in the main travel seasons.
They also offer beautiful appartments and bungalows in and around Marrakech.