I was there in January this year too! I only thought it was cold when we went into the mountains, but even then I didn't have my coat with me. We'd just come from Budapest and Prague though, which were pretty chilly.
We went to Marrakech, Chefchaouen and Rabat. I would probably only recommend Marrakech for you- Rabat is a bit too European for atmospheric wandering, and while Chefchaouen is beautiful and great for wandering (we spent our whole time there wandering, without any particular 'sights' in mind), it's hard to get to and we were pretty aggressively hassled there. I'm pretty familiar with getting off the beaten path or whatever, so I'm used to being hassled to some extent, but this was by far the worst I've experienced. Marrakech is great though. It's different enough that you can happily wander around and enjoy the atmosphere, but tourism is also well-developed enough that no one really cares that you're foreign and won't bother you. I would feel totally safe taking kids there. And yeah, Earth Cafe is a must!
We stayed at a guesthouse there, which might be a bit too basic for your needs but it was great so I'll recommend it anyway- Douarskoll Guesthouse
. The place itself isn't really anything that special, but the owner is the best guy ever, he's super funny and helpful and always made us huge breakfasts, even on the morning when we had to leave at 4am.
I've heard a lot about Essaouira being relaxing and easy-going, but we didn't get down there. It won't be the busy season since it's a beach town and it'll be mid-winter, but maybe that's a good thing.