Basically I want one close to where fast travel to the city puts you, ideally with storage/bed on first floor or easy to get to, and with an enchanting thing.

I already checked out Solitude's, but I didn't like the interior really, kind of obnoxious lighting and the bed/storage are on the second floor plus it's a distance away from the entrance.

The only other one I can think of is Whiterun and Markarth but Markarth could be a Stormcloak city.

Markarth is indeed Stormcloak.

Riften is as well. Windhelm too.

Arg.