Where do you begin to find the right website? You start with the area of interest that is calling out to you. The Internet is no different than the real world in a lot of ways. If you do something online that you don't enjoy, then you can't expect to be profitable at it. That doesn't necessarily mean that if you're a movie buff, you go after a movie website, but it could. It just depends on what your plan for monetization is, and how you plan to implement it. If you can find a way to implement your plan that is exciting and fun, then you could very well be where you want to be before you know it.
So start with your passion. Search online at social hubs. Places like Twitter allow you to run searches for specific search terms related to what you are looking for, and you can see in real time the "tweeters," who are "tweeting" about that very thing. Send a follow. Establish a relationship. Ask for referrals. If that doesn't work, you may wish to check with your hosting company and see what sites are available in your area(s) of expertise or interest. Once you have a list, start sending out some emails. Carefully craft what you are going to say and try not to sound too overeager. You don't want to give up your bargaining power with a little overzealous behavior.
It's best to start with a simple query that shows a general interest and that explains how you came to find out about the site being for sale. Say that you were in the market for a Movie site, for instance, and that your hosting company or a professional colleague pointed you in the direction of several that might be interested in selling. Once the dialog is established, make sure you get traffic numbers and other statistics to ensure that you're making a good purchase. Then, put your best offer forward based on what you will be comfortable paying.