Onsens & Snow Monkeys (April/May)

My sister and I are planning a trip to Japan. We have three weeks. During this time we would like to stay in a relaxing spot at a nice onsen. It seems like there are lots of areas for this.

A friend recommended Mount Koya Monastery. Is this worth the trip?

I also saw Yudanaka Onsen/Shibu Onsen which might be good as it is near the monkeys. We are going in late April/early May though, so I do not know whether it is worth the trip to see them without snow?

Kinosaki-Onsen also looked nice.

Does anyone have any recommendations? Would you recommend staying 2 nights rather than 1 if time allows?

A friend recommended Mount Koya Monastery. Is this worth the trip?

Yes, it is one of the highest ranked activities on japan-guide.com. But it has neither onsen nor monkeys.

I also saw Yudanaka Onsen/Shibu Onsen which might be good as it is near the monkeys. We are going in late April/early May though, so I do not know whether it is worth the trip to see them without snow?

I personally think they are worth a visit at any time of the year.

Kinosaki-Onsen also looked nice.

That is, indeed, one of the best traditional onsen towns.

Does anyone have any recommendations?

The following page lists some of Japan's best onsen. I recommend you read on them and pick the one(s) that look most attractive to you personally:
http://www.japan-guide.com/e/e2292_where.html

Would you recommend staying 2 nights rather than 1 if time allows?

It depends on the place, access situation, amount of local attractions. But if you have the time and budget and like to relax, then two nights would be nice.

Thank you for your help, Uji!