There are tons of museums to go to in Peru, from art museums, to gold, or cultural museums. Take a look at Enjoy Peru or Peru Cultural for more information about the different museums here in Peru. You can find some more information about museums in Lima at Lima Easy.
You can find more info in Culture and Free time activities. The lastest events can be found in Upcoming Events. You can find more information about cultural centers, in Peruvian Cultural Centers.
One tip to remember is that speaking Spanish will help you greatly. You'll be treated differently than if you speak English all the time, it'll help you assimilate, and you'll be able to communicate easier. If you're looking to learn Spanish, check out Fluenz Spanish, Rosetta Stone, and Synergy Spanish.
The Ultimate Peru List recommends: