The best option for you is to stay in a Riad. It depends on your budget, but as Marrakech is not that expensive, you can find acceptable Riads starting at 30€, and better ones for 60€. If you have some Booking Genius discount, you can opt for up to 10-15 % discount on the price, or if you know someone owning a travel agency, you can opt for a 20€ discount per night.
The Riad is a typical Moroccan type of house, which owns a patio normally with a pool, but not always, right in the middle of the building. For your stay in Marrakech be more authentic, an stay in a Riad will be a recommendable must!
My personal recommendation for a GOOD Riad, not short on comfort, neither fitting a luxurious standard, will be: Riad Challa. For 60€ per night, you can enjoy of an authentic Riad very close to the Medina of the city.