Actually, based on what I've seen, you get the monkey that is weak to your starter, and you can go to the Abandoned Lot of Dreams and get the monkey whenever. However, if I were playing the game, I'd get the monkey before you go in Dento's gym as it would give you an advantage over his/one of his brothers's monkey.
I'm not entirely sure what's there, but I do know that you encounter Team Plasma there and you can catch a special Musharna every Friday.