One of the easiest ways to find keywords you have a higher likelihood of being able to hit page one on. Is just looking at similar domains, that have a lower domain authority score than you. See what keywords they are ranking for, then writing a better article then they did.
If you have not already installed the mozbar. Then go ahead and install the chrome extension. You will also need to create a free account with Moz, for the tool to work.
Turn the Extension on, and head to google, bing, yahoo, or any other search engine.
You will want to search for keywords that are related to the niche you are in. Looking for websites that have a lower Domain authority, and perhaps low inbound links to that inner page.
Dont pull sites that have a super low DA, as they wont be ranking for many keywords. Find websites that have a lower, or similar Domain authority score to your website. You are just manually building a list of domains you can compete with.
After you have found a few domains you feel you could out write & rank. Start searching for what keywords they also rank for.
Once you know what keywords the low authority websites are getting traffic from. Start writing articles for those topics. Build a few inbound links to the article and enjoy the easy traffic.
Ahrefs used to be the place to easily see what keywords they are in the top 50 with, now that isnt an option. One way you could do this is export a google PPC keyword list, and use scrapebox to find your list of low comp domains within the first 50 results. Any keyword that gets a hit, is one worth looking into.