How do I lower nitrites in my fish tank when my tap water is very high in nitrites?

Plants plants plants ! :) if you have a low watt light bulb buy some java moss , Anubis , hornwort works the best to reduce nitrates ! With all those plants you won't need any new substrate your water and fish waists is enough nutrients for them , also if you buy one hornwort it will over grow you cut it and plant it back into the tank for multiplying affect it grows like crazy ! Good luck :) also you can do a 40% water change once week and 20 % water change in between water changes like 40 change on a Friday and 20 water change on a Tuesday

Either use a different water source or use a nitrite remover on the water before you put it in the tank.

How high are we talking?