How can I get an entry's child category, and not the parent category?
Your Categories field (entry.chooseLocation) is an Element Criteria Model. It's exactly the same as if you'd done something like this...

craft.categories.group('myGroup')


The Element Criteria Model (ECM) is an important concept in Craft, because it's the driver for most content handling. Once you've got a bearing on what the ECM is, you can use it fairly consistently.

For example, just like craft.entries, you can apply .find, .first, and other methods to retrieve a specific subset of elements. And depending on the element type, you can chain other filtering methods in between...

craft.categories.group('myGroup').limit(3).find()


Returning to your question, entry.chooseLocation will be an ECM for Categories. So it's just a matter of filtering it appropriately.

{% for category in entry.chooseLocation.level(2).find() %}


Here is the full list of filtering options you can use on a Categories ECM.