You may purchase a wall mounted oscillating fan but you will find that because they are wall mounted, they tend to not have the 120 degree side to side oscillation that you may be seeking, though some few fans have been specifically engineered to offer you this much Oscillation. These types of models tend to be rather expensive, so the wall mounted oscillating fan will usually oscillate 90 degrees although if that feature is of supreme importance to you, you should check with the manufacturer prior to purchase.
A wall mounted oscillating fan will ordinarily come in a plethora of colors and styles, from the commercial fan that is made of durable metal with a tight metal grid to prevent injury such as what's seen in schools, to the designer types which are often made of Plastic including plastic fan blades that may actually come as see through blades or be colored to match the rest of the fan. These fans will come in designer colors too, such as Ivory, Dark Brown, Forest Green, Nickel or Chrome. You may also find them in Aqua, Gray, Turquoise, Dark Blue and even in various wrinkled finishes in paint or an industrial white powder coat finish. Or, you may opt for a very sophisticated textured bronze finish Naturally fans of almost any color can now be produced in plastic
Many commercial oscillating fans will have a three position ratchet setting in order to direct the desired airflow into the room when that fan happens to be mounted close to a corner. This is the same reason why a wall mounted oscillating fan usually has to capability of being locked into a non-oscillating position.
There is a possibility that a oscillating fan will have a remote control to run it, although many of the earlier ones did not have this feature. The newer ones seem to be offering that element though.
In dining areas, many people prefer oscillating fan as opposed to a ceiling fan, as it will not blow down directly on your food cooling it off prematurely. Of course having a wall-mounted fan also means that you save on precious floor space and never have electric cords laying around to trip you up either.
Of course most wall mounted oscillating fans have an adjustment for angling them down, although many people need to adjust their fan changing the range of oscillation from a dead center position to the left or to the right to some extent. If you will investigate the schematics included with your fan you may often find another screw that enables this kind of adjustment. After loosing it to some extent, you can usually move the fan to the left or right, until you hear a ratchet-click, then you may tighten said screw.
Today you even have an indoor / outdoor wall mounted oscillating fan available. They are waterproof and so are UL certified for specific use outdoors.