I get itchy eyes and runny nose when i go down to my basement. what could cause that?

Allergies: Basements and other dark damp places may harbor allergens such as molds. These can be powerful allergens and cause intense itching. Be sure to check for these or water leakage. Just wear a mask with good ventilation or call a professional if you smell a musty odor.

Mold, dust, allergy: Basements can harbor mold, dust, and animal dander. Often, there is poor air circulation which creates the problem. If you cannot or do not want to avoid going to the basement, have it professionally cleaned and evaluated for mold. Using antihistamine eye drops may help the symptoms, but the root cuase will still be there.

Mold spores: Mold is likely. Install an electrostatic air filter / cleaner and wash the element in the dishwasher monthly with a tablespoon of household bleach. That will kill the mold. Also clean everything out and mop with a fungicide solution purchased at home depot or other commercial store or hire someone to professionally clean it. You could also have a pest or animal problem or birds.

Possible allergy: Could be an allergy to dust or mold.