Recent surveys of home buyers by the National Association of Realtors® show that around 90% of them used the Internet in their search for the home they purchased. And, there are plenty of websites that are vying for your attention as a home buyer.
Realtor.com has the largest group of homes listed on Realtor websites, members of the National Association of Realtors. That's because they are fed electronically to Realtor.com at least daily by the local MLS, Multiple Listing Services. It would seem that this would be the best place to search in that case. Well, you're not interested in searching the entire country, so having them all available isn't an advantage. Also, while listings are represented free for the listing agents on the site, they are ranked in your searches based on criteria that include payment for better positioning, how many images are present, and more. So, the site visitor isn't always seeing the homes sorted in the way that's most efficient for their search.
To get the same listings on a local basis, find a local Realtor site with an IDX search, and most are set up this way. IDX, Internet Data Exchange, is an agreement among the brokers to show all of their listings on every participating site. And, while it can give precedence in search results to that broker's listings, that's usually the only manipulation of how you see them.
Of course, if you want to see FSBO, For Sale By Owner, listings, there are other sites out there that allow those sellers to display their properties. You won't find FSBO homes on the IDX sites.