There's not a lot really close to the arena yet, since the associated development projects are scheduled to lag behind the arena opening. Your best bet is something downtown, IMO, near Woodward for an easy walk, public transit, or Uber.
The Westin Book Cadillac is our go-to when we're in Detroit for an event. The rooms are large and comfortable, they have an indoor pool, and the steakhouse in the lobby is really good. It is just a bit under a mile from LCA, straight up Woodward for most of the way so the whole walk is on busy, well-traveled, well-lit streets. I haven't stayed there since the Q-Line rail opened, but that also runs right up Woodward so if you didn't feel like walking the whole way you could take the train.
The hotel in the Whitney Building would be a bit closer still, right on Woodward to make catching the Q Line even easier, and it looks fabulous but is a bit pricier so we haven't stayed there yet. I think that one is Aloft brand?