There are 3 Anytime Fitness in Nagoya in convenient locations for tourists. However, all of them are a bit far from the main area of Nagoya. As there are many reasonable hotels with gyms in Nagoya, it might be better to check out the hotels with gyms first if you want to stay in a convenient location. Check out my recommendations of hotels with gym in Nagoya from here.
Anytime Fitness Nagoyasakae is in the entertainment area with many restaurants and shops. There are many reasonable hotels around here. Reasonable hotel nearby is Apa Hotel Nagoya Sakae. It is within 2 min walking distance from the gym, and it has a large public bath (great after workout !)
Anytime Fitness Shinsakaemachi is also in convenient area. Reasonable hotel nearby is Mielparque Nagoya. It is an old school comfortable hotel.
Anytime Fitness Meijyokoen is close to the Nagoya’s most popular tourist spot; Nagoya castle. You can go to this gym and visit Nagoya castle after workout!. As there are not many restaurants and hotels nearby Nagoya castle, it would be better to stay around the main area (Sakae area).