How to efficiently get a mention of your just accepted paper in journals like Nature and Science
If you think this discovery was big enough for Nature or Science then why didn't you send the article to either of these journals?

You can't tell people what to be excited about and if the work is good enough then it will make its own headlines.

In the mean time, speaking to your university press officer seems like a good start and they can put something out to local newspapers. If its big enough, then it'll be picked up by bigger outlets.