There are a few geomorphological methods that could produce similar effects. You even mentioned a range that is produced by one of them. There are different physical scales for each, but most of them are produced by one main process: Tectonic activity. There's one other that I can also think of that can be caused by either tectonic activity or another process.
Generally what will happen is if you have hills surrounding a valley, you will get watercourses running from the hills to the valley, and these will meet to produce a larger water-course. Temperate climates can be very wet - the Pacific North West of the USA gets about 200 inches (16 feet/5 metres) of rainfall each year. Mountains tend to get more precipitation if they disrupt wet airflow from seas and taller mountains are cooler, so cause more precipitation. However, too tall and it'll be locked up as ice/snow.
The Himalaya and associated mountain ranges (Hindu Kush, Karakoram, Pamir) are produced by the Indian plate crashing into the Eurasian plate. These produce, what is effectively a ring of mountains that separate the subcontinent (India, Pakistan, Bangladesh etc) from Eurasia. These sorts of tectonic events generally operate on continental scale, producing very extended mountain ranges in both height and depth (i.e. not a single line of mountains; many many lines of mountains covering huge area). One of the world's greatest rivers is the result of this event - the Ganges.
I don't see why it couldn't happen on a smaller scale, with much of the plate(s) underwater and only small portions poking up and producing your island with mountains on the up-lifted parts, but the depth of the ranges might preclude this.
On a similar scale, tectonics can also produce separation events. The classic case here is the East Africa Rift, where the Somali Plate is separating from the African Plate. This produces a depression in the land, which is surrounded by the sides of the valley - now you might be thinking narrow here. the Rift is about 4000 miles (6400 km) long and about 30 miles (50 km) across, with a drop of 600-900 metres (~2000-3000 feet) in depth from the plateaus on either side.
On a smaller scale, plate tectonics produces earthquake zones due to land masses sliding around. These go by various names:
Horst-Graben (German for Range-Valley) structures produce valleys with hills around and can end at ranges. The East Africa Rift is a very large-scale horst-graben structure; but they come much smaller too. These are found in many areas of the world.
Strike-slip faults can result in a valley between two ranges, particularly where faults don't lie parallel to each-other. The Wellington and surrounding areas in New Zealand sits on a system like this. Check out a satellite view or topographical overlay on a map website/app to see.
Volcanism. Climate has nothing to do with volcanism - Iceland is famous for its volcanoes, and Antarctica has a couple of massive ones - Mts Erebus, Terror are both well over 3000 m (10,000 feet) tall. Ring structures from calderas are common around the world, as another answer pointed out.
The final mechanism I can think of is sea-level change. In many parts of the world you can find high-level plateaus that have sea-shells etc embedded in the rocks. For example, the central part of the USA, was, between the Cretaceous to the Paleocene, occupied by a sea known as the Western Interior Seaway. Obviously this is no longer the case because of sea-level change. The changes that can cause the sea-level to change are either through tectonic uplift, but also through climate change. During the ice-ages, vast amounts of water were solidified in the form of ice, lowering the sea-level, which could leave a former bay out of the water.
Another change in the opposite direction is that with warming of the climate, an valley system formed by glacial action could be left without ice as the glacier(s) melted. Fjords are examples of formerly glaciated valleys, though since submerged in water. The McMurdo Dry Valleys in Antarctica are also examples of formerly fully glaciated valleys, though most of them still have some glacier left at the head. I am sure there are plenty of other places around the world with similar systems as a result of glaciation and climate change.