Probably the most famous US observatory is the huge complex at Kitt Peak National Observatory (part of the National Optical Astronomy Observatory network) outside of Tucson, Arizona.  Institutions the world over, and a rich guy, have telescopes here.  As a partly publicly funded facility, you can tour the grounds, and even reserve time on a 16" scope for public use. The summit is at 6875 feet.

Below is a mosaic I took from the public viewing balcony in the 4-meter (158 inch) Nicholas U. Mayall telescope dome that shows most of the other scopes.  Many scopes here, such as the big Mayall scope completed in 1970, date from the pre-alt-azimuth mounting days, and so have typical, classic domes.  In 1997, twenty-two vents were installed in the dome for improved air circulation and temperature control. It is used primarily for infrared and faint visible light observations such as determining the rotation curves of distant galaxies and the dynamical structure of elliptical
galaxies such as M87 and M49.

The WIYN scope, in the far upper right background, is one of the newer boxy, short focal length, large diameter types built today.  The McMath-Pierce solar scope (tilted triangle a far left), which, as discussed on the NSO page, can have unique designs typical of solar observing.  The structure includes a tower nearly 100 feet in height surmounted by a 3-mirror heliostat that collects light and directs it down the tunnel that slants two hundred feet to the ground where the sun is viewed at the prime focus. Unlike other solar telescopes, the McMath-Pierce, which normally studies sunspots and solar spectra, is sensitive enough to observe bright stars at night! 

There are many more smaller but specialized telescopic facilities here, including the Warner & Swasey Observatory Burrell Schmidt Telescope of my alma mater Case Western Reserve U.  See for tons more info.

Here's the 18-story Mayall scope dome (above), and part of the scope (below left, it's largely blocked by the old-style equatorial mount).  Because I'm lucky enough to know two folks who work there, I got to tour the inside of the Mayall and WIYN (below right) observatories!  Most large scopes these days are compact and boxy and barely fit inside their domes, so it's hard to photograph them as you are invariably too close, as was the case with the 3.5-meter WIYN.  By comparison to the 4-meter Mayall, with a moving weight of 375 tons, the only slightly smaller WIYN weighs only 46 tons.  Gone too are the days when the astronomer would be at the eyepiece or even in the observatory, the quarters are so tight and the instruments so sensitive that his or her body heat would ruin the observing, especially in the tight quarters of the modern compact domes and adaptive optics.  Note the large openings in all sides of the comparatively tiny WIYN dome to facilitate equilibration of the inside and outside air.  All the electronics are kept in isolated, air-conditioned rooms.  With better thermal control and adaptive optics, the WIYN can outperform the larger Mayall.