There are some---Chavín de Huántar is probably the best known---but nothing like MP. Huaraz is best known for trekking. May is a good month as the rainy season tapers off in April so you can expect dry weather with some green left over from the rains.

If you want culture without the MP crowds, consider Kuelap. It's getting more popular and will some day be over-run, but it hasn't reached that point yet. It's in the north; the nearest major population center is Chachapoyas.