Volcanoes might well produce a number of such bowls. There are several of them around Earth. It does not even require a massive explosive event. As L.Dutch mentioned, Yellowstone is such a place. There is also such a valley in New Mexico called Valles Caldera. It's really quite picturesque.
Smaller round valleys can be formed by glacier action. If there is a vertical hole in a glacier that allows melt water to cascade down, it can erode a fairly round hole. An example is Crawford Lake, Ontario, Canada. It's approximately 50 meters across and 22 meters deep. Possibly you could squeeze a small orchard in there if it wasn't full of water.
Also you could get quite substantial valleys, though probably less bowl shaped, from subsidence. For example, the Great Rift in Africa. Or the central portion of New Mexico. This is a screen grab of a Google 3D satellite image of the area near Alamogordo. This is because the central portion of New Mexico subsided relative to the eastern portion. It can make sunsets quite interesting since this faces west. Weather, particularly temperature, can change quite drastically from the top to the bottom.
A bowl 100's of km across provides precious little protection from the weather. In such a situation you would have to examine things pretty carefully to even be aware you were in a bowl. For example, you might not be able to see the ring from the middle, depending on the planet's curvature. A dust storm will go right over a line of mountains unless it's very tall. The ring around a volcanic crater usually isn't particularly tall. You would get a larger effect from being at lower altitude than from being protected by the ring. Lower altitude means denser air.