I agree with the above posters. What hotel is it? I have had bows/rifles in MANY motel rooms over the years. Some motels even offer "deer hunter specials" in the fall. Never, ever heard of not being able to have one in the room. I can understand them not wanting you to shoot in the room, but possession shouldn't be an issue.
There is an indoor range on Bonny Oakes drive I think. Alex has sold the owner a Fox bow or two over the years. Next month there will be an Old Fartes shoot in Crossville TN, about 90 minutes out of Chattanooga. I live about an hour out of Chatt as does Rob. NoCams - Jimmy is about 45 minutes to your west, Don and Skyler are about an hour away.