How many colleges are there, anyway? If you're talking about the US, no one really knows. There are a lot of reasons for this, some of which are definitional: Do you include cosmetology colleges? Welding schools? Schools of massage therapy? IPEDS includes many post-secondary options for students that don't offer an English or a history major. So it's complicated.
You can go to IPEDS and make your selection using "All institutions" and you'll find the "answer" is 6,527, but that's not quite right: That's how many colleges are in IPEDS, and you only have to be in IPEDS if you accept Title IV funding. There are lots of schools in the US, like The Classical College of Baton Rouge, Louisiana; or John Witherspoon College of Rapid City, South Dakota; or Wyoming Catholic College of Lander, Wyoming, that don't take Title IV funding, and thus don't report to IPEDS. And to complicate matters, there are colleges that don't accept Title IV funding but report to IPEDS anyway, like Hillsdale College of Hillsdale, Michigan.
If you're not yet confused, you will be. And what makes it more complicated is some of the things in IPEDS are not what we think of as colleges, such as "The University of Alabama System" which is an administrative body, enrolling no students of any sort.
But this is probably as close as you'll get. To start, I downloaded all 6,527 institutions in IPEDS, and then took some out: Colleges listed as inactive in 2019, or colleges with zero enrollments, for instance. That leaves us with 6,314.
Now, you can decide what your definition of a college is and get your count.
In this visualization, you'll see two bar charts: On top, for reference, is all 6,314 left standing after my selections. Then, using the filters, you can see how many are in your set on the second bar chart, below the first. Want private, for-profit, two-year? There are 585. Want colleges affiliated with the Reform Church in America? There are five. Once you make your selection, you can see the list of them near the bottom (scroll to see them all).
Once you have your selection (like the 795 public, four-year universities), you can split them out using the "Break out" control at top right. Choose "Region" for instance, and you'll see how many of those 795 four-year public institutions are on the west coast (122).
It's fun to find your own answer, I think. I hope you enjoy this.