You can locate a lot of relevant pages simply by searching within Facebook itself. You just type your chosen keywords into the search box and click on the Pages button in the search filters. But if you are really determined to find a lot of pages then this method probably won't supply you with enough of them on its own.
Google, Bing, Yahoo
So, you should then move outside the "walled garden" of Facebook and search on Google, Bing and Yahoo as well. Just type in your chosen keywords along with "Facebook page". This will supply mixed results, but if you do it often enough you're sure to find ones you haven't seen already.
The pages themselves
If you've used both these techniques then you would have accumulated quite a few of them. And you can use these to find even more. Just look at the likes of each of these pages. They usually list several, sometimes scores of other pages in their niche. Helpfully, Facebook tells you which ones you've like already. It's kind of like going from blog to blog via the comments. You'll never run out of them.
And speaking of blog-hopping: That's yet another way to find new Facebook pages. This is because a substantial proportion of bloggers already have their own pages. They almost always have badges for them (much as I have on this one). So, make sure that you're logged into Facebook while you're looking for new blogs. You can join them as quickly as you find them, then.
You can also find new pages via the contributions of others. You'll see these in the top right hand corner of each page as well as below each update in the form of likes and comments. A good percentage of them will be from other pages. And if they are from individuals, you can check them out too. A fair proportion of them will have liked several more pages in the same niche as the one they've commented on or shared a link with.
If you use several of these methods to find new Facebook pages, before long you'll have hundreds of them to interact with as your own. You can engage with them repeatedly and thereby get on the radar of many more people.