I wouldn't really be too concerned about the nitrate level. Commercial fish growers routinely have nitrate levels as high as 150ppm. Live plants actually don't do that great of a job of removing nitrates, they actually make better use of ammonia. Not to say that plants won't help, I'm an advocate of using plants in the tank for a more natural environment.
Anyway's, given that your tap water contains some nitrate, to get the level in the tank down, you should do more frequent and larger water changes.