I would definitely stick to keeping it alphabetical, unless you have clear data or user research that says not to.
It's a little difficult to know specifically without a bit more context. Will your users be selecting a region as part of registering an account, entering their address, booking an event, or something else?
For instance, if your data/research shows that the majority of users are more likely to select one or two regions from the list compared to the others, you could try placing those first in the list, then listing all the others alphabetically below that.
Many account registration forms do this. For example, they will place United Kingdom and United States first in the list, then list all other countries alphabetically. They do this because, in this example, they know that the majority of users are likely to choose one of these countries. Therefore, it's easier for these users to have them listed at the top, rather than having to scroll through a list of 150+ countries.
Finally, I would be vary wary of allowing users to choose regions by clicking on the map directly, for a few reasons:
- Awareness of geography: not all users will be able to identify where each region is on a map.
- Accessibility: some users may be elderly, have poor eyesight, or difficulty with fine motor skills. Choosing regions on a map is difficult for such users.
- Region size: some regions may be very small in your map, being only a few pixels in size. They will increase chances of errors and could cause frustration.
- Device support: It will be very difficult to implement this for touchscreen/mobile devices without some sort of pinch/zoom functionality. This will likely be expensive to develop.
Hope this helps!