I am not sure what a closet walkable hotel is. There aren't really any hotels that a walkable distance nearby. You would have the best luck looking to the southwest for hotels.
The Asbury is pretty close.
We stayed at the Empress Hotel and it was great! We walked to the concert and back in the windy cold and it wasn't that bad. Definitely doable on a cold day, even better walk on a beautiful day. I would recommend staying at the Empress if you're going to the HOI.
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