I'd really like to see monkeys, but not in captivity, or at least try.
is there a location outside tokyo where this could be possible?
If you meant wild monkeys, well, these are old data but you can see the Japanese Environment Agency's distribution areas from here
the data written in this document (P18), in Tōkyō' Hachijōji-shi, Akiruno-shi, Hinoharamura and Okutamamachi seem to have lots of damages to farm products so it seems you can find monkeys also there.
For me, I kind of feel you'll find them also in Tochigi-ken!
In Izu' "Hagachizakien" or in Nakano-ken' "Jigokudani Onsen" or in Kyōto' "Arashiyama Monkey Park".
In winter, at Jigokudani Onsen, monkey enter into the pools of the onsen so I think it's really interesting. While in Izu and Arashiyama you can feed them. They're really amazing place to visit also with the family, so try to go there if you have the chance.