You may find that at times, trying to find a new niche is actually not the problem at all.
But rather, it's trying to choose among several good niche topics. So how do you choose which one to start with?
I believe that the most important aspects to consider are your interest in the niche and the future potential growth of the winning choice.
First, you should consider if the niche is an evergreen choice and not subject to temporary highs (i.e. Valentine's Day, Mother's Day, Christmas, etc), since you would likely prefer to earn a steady annual income.
One of the handiest tricks to identifying an evergreen niche is by using the Google Trends at http://www.google.com/trends.
Note, that if your niche has more than one word be sure to surround those words with apostrophes. And you want to compare more than one niche at a time, then separate each set of keywords by a comma.(i.e. "dog breeds", "dog names","dog training")
The next element to consider is if the niche has the potential for growth through various backend products. If your niche were "Dog Training", then you should be building relationships with your clients and, over time, expose them to other "Dog" related products. These could include such areas as "Dog Grooming", "Dog Flea Control" and so on.
When choosing your winning niche, be sure to also identify who your target market will be. In the example of "Dog Training", will your market audience be young mothers with school aged children or recent widowers who have a dog for companionship.
Once you have identified an evergreen niche and your target audience, then you can begin assembling some of the blueprint components for your new website.