Brown spots on new stainless steel pot
"Stainless" steel is an exaggeration at best. It will stain. Chances are you have some level of mineralization in your water (hard water), and that's what's causing the discoloration. 

If it really bothers you you can use Bar Keepers friend or something similar to polish it, but it's unlikely that anything that doesn't come off with normal washing will come off in your food.