I was there in March so here's some of my thoughts.
Stay in a Riad in the old city. Yes, there is the Four Seasons and other resorts in the new city but you'll miss out on the authentic Marrakech. OK, they won't have a fancy restaurant or a spa or even a pool, but sometimes you need to sacrifice that for amazing service and locations.
I stayed in Riad Altair and it's about a 15 minute walk to Jemaa El-Fnar which is the main market square in the city. During the day it's home to monkey trainers, snake charmers (listen for pipes if you want to avoid) along with various stalls selling fresh orange juice, dried fruit and spices. From around 6pm it becomes an open-air restaurant selling all manner of meals to visitors for very reasonable prices.
I'm sure it is possible to get French or Italian cuisine but could not say if it will be good and/or cheap. I lived on tagine and the most I paid was 45 MAD and it was freshly made and plentiful.
If you do stay in a Riad, be mindful that as a Sunni Islam country you will have the Call to Prayer sounding across the old city, especially the Fajr which comes well before sunrise. It never failed to wake me, but I soon nodded of again after. I could even recite some of it by the last morning.
One place to visit is Jardin Majorelle. It's a little garden in the old city famous for being where the ashes of Yves Saint Lauren were scattered. From the Riad it was a 30 minute slow walk. Ignore Menara Gardens, olive groves surrounding a murky irrigation pond.
Can't speak for the 737 as I was on an A320. A full iPad made up for no IFE.
One other tip. Try to pay for a taxi with decent quality notes. I had one start getting ansty as the note I gave was grubby (got it from another taxi). Luckily the number of tourist police at the destination prevented him getting out of hand. Unless you need a larger one, only get a petite taxi as they're cheaper and just as fast.
Thanks
Darren