There is no fitness gym in the Haneda International airport buildings but If you have a half day before flying out (for transit etc..), then there are some options.
Gold Gym Hamamatsucho : Open Mon-Fri 7.00-23.30, Sat-Sun 9.00-22.00. Closed 3rd Monday of the month. Day pass costs JPY3,960 per visit. For long-stay tourists, they have Traveler's passport. It costs JPY11,000 for 10 days. You need to bring your passport for ID check. See the official gym website.
To avoid embarrassment and disappointment at the gym, please read Tips and etiquette before going to the gym in Japan.
Recommendation: If you want to work out before flying out, the best choice is Gold Gym Hamamatsucho. This gym is located 2 minutes’ walk from Hamamatsucho station where there is an express train (monorail) to Haneda airport. It takes about 30 mins. If you have a half day at the airport for transit etc.. then it is a great idea to go to this gym.
If you are an Anytime Fitness Member in your home country, you can use 1,200+ Anytime Fitness gyms in Japan 24/7 for free (your home country’s membership covers the cost). You can use the same security key tag to enter. There is no Anytime Fitness gym within the Narita Airport. Nearest one is Anytime Fitness Ootorii .From Haneda Airport terminal 2, take a Keikyu Airport line to Anahori Inari station (12 mins) and it takes 1 min walk from the station to the gym (Purple icons on the map).
If you have a connecting flight to other cities in Japan and want to stay close to Haneda Airport, Villa Fontaine Grand Haneda Airport is a great — and pretty much the only — choice for fitness-minded travelers. This large hotel is connected directly to Terminal 3, and you can easily reach Terminals 1 and 2 via the free shuttle bus for domestic flights. The hotel has a good gym, though unfortunately you have to pay JPY2,200 even as a hotel guest. It's equipped with 10 cardio machines, 10 weight machines, and free weights ranging from 1kg to 22kg, plus a spacious stretching area.There are many shops and restaurants within airport building. Check out the review and price !