I think a lot of Czech people are misunderstanding the word, Outlet. Outlet is not a single store which sells many kinds of brands for affordable prices. Outlets are stores which manufactures sell to the customers directly. Then, usually several outlet stores are group together at outlet malls.
Japanese love shopping as like Americans and therefore there are many outlet malls in Japan. There are 7 outlet malls in Tokyo metropolitan area and another 7 in Osaka-Kobe-Kyoto metropolitan area. Which means that you have a chance to visit these outlets during your stay in Japan.
The closest one is Mitsui Outlet Park Makuhari which can be reached from Tokyo station by limited express Wakashio in 30 minutes. The limited express calls at Kaihin-Makuhari station and it is just a couple minutes to the outlet park on foot.
However, if you want to do shopping and sightseeing together, I recommend to visit Gotemba Premium outlet in Gotemba, Shizuoka prefecture. Gotemba city is located at the foot of Mt.Fuji and you can enjoy the view of Mt. Fuji during the shopping.
Gotemba Premium Outlet has shuttle buses from Gotemba station on JR Gotemba line. If you are staying in Shinjuku area, take a limited express Asagiri(the name will be changed to limited express Mr.Fuji(Fujisan) on 17 March 18) from Odakyu Shinjuku station(for JR pass holders, you have to pay the supplement for Odakyu line) to Gotemba station. Or if you are staying around Tokyo or Shinagawa stations, take JR Tokaido line bound for Kozu, Atami or Odawara and transfer to JR Gotemba line at Kozu station. It takes roughly 2 hours from Tokyo station.
The outlet is also connected to Kawaguchiko(Kawaguchi lake) station and Fujisan station on Fujikyuko line in Yamanashi prefecture by bus. Therefore, you can first go to Kawaguchiko and then later to the outlet by bus or v.v. In this case, take limited express Kaiji to Otsuki station and change to Fujikyuko line.
Weekends and holiday seasons will be crowded and therefore I recommend to visit during weekdays.