These guys are on the top over everyone's list. BBC has made documentaries about them, Japan promotes them, everyone goes here, yes!
And I totally understand why. It is a fun place to walk through the mountain path during all seasons. The monkeys are there to see all year round.
So, why am I including it on my "local" guide? Because I know people like to go and I want to give you a tip!
Go early. I know it sounds cliche but this is what you need to do in order to avoid the bus loads of tourists. If you want to make the most of this place you need to drive a car and arrive right at opening time. I arrive around 8:30am by car and get to the park entrance (20-30 min walk to entrance) by 9am when it opens. There are usually only a few cars in the morning as the majority of people visit by tour bus. It's easily the best time to be there or late afternoon before closing.
FYI buses start arriving about 10am and when they do it can be chaos.
One other thing which is nice to level expectations: the monkeys are not as wild as promoted. They are fed to keep them as an attraction for tourism. That, and the hot spring is man made for tourism (originally built to entice monkeys away from the local onsen hotel).
Overall, it is great and worth a visit if you time it right. Who wouldn't want to see monkeys chilling in a hot spring?
Enjoy!