Seems like an easy question: There are 7,284 post-secondary options in the US.
But everyone has a different definition of what they want when they ask for a count of colleges. This should give you some clearer sense of the right answer for you.
At top left is "The Answer," and that will not change as you navigate through this. But you can use the controls here to change the number of colleges and universities you're looking at, and to change how they're broken out.
Those controls change the number (in orange, at top) and the splits.
For instance, at the far right, on the control labeled "Region, choose "Great Lakes," and you'll see that there are 1,079. On the gray box at top right, choose "State" and you'll see 354 in Ohio. Under "Control of Institution" choose "Public" and you'll get 266. And so on. Now break out by "Campus Location" and see most are located in cities.
The reset button is at lower right.
I hope this is helpful to you as you wonder about the shape and size of American higher education.