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I stayed at the La Quinta Inn the last time I was in Bowling Green. Top rated at TripAdvisor.com and reasonable pricing. New, clean and a spacious lobby etc. with a great free breakfast in a dedicated room with plenty of seating. Also next door(short walk) is the Cracker Barrel. Just east of the motel is a new self service car wash to keep your Corvette clean while in Bowling Green. Shell station at the corner.
Just about all the decent motels, restaurants, shopping, etc are located at exit #22. Not much located at the museum exit #28.
I will also say the LaQuinta in Bowling Green is a nice place to stay. My wife and I travel with our dog and they allow pets. The hotel is very clean and if you like your hasbrowns smothered and covered there is a Waffle House next door! See you at the "Bash".