The path shown in the error dialog shows that you are trying to save the default preferences (the left hand pane). The short answer to your question is: Don't do that; you only need to save the file on the right; the file on the left should be un-editable and thus needs no saving.
The file in question is a part of the
Default package, which is not represented by loose files in the
Packages folder; as such there is no
Packages/Default folder, so your attempt to save the file fails and you see that message; the
No such file or directory is referring to the
Simplistically speaking, the settings that end up getting used are the settings on the left, except that any you specifically add to your own settings on the right take precedence, so you only need to modify your own settings (and even then, only when the default value is not what you want).
That's done on purpose specifically so that you can upgrade/reinstall Sublime without messing with any of your settings. Among other things this means that removing and reinstalling Sublime is generally fairly unlikely to actually solve any problem that you might be having, unless the problem is that the actual application install got corrupted somehow.
If you select
Sublime Text > Preferences > Browse Packages... from the main menu (on Windows/Linux this is just
Preferences > Browse Packages...), a file browser will open showing you the contents of your
Packages folder. If you examine the path in question, you're going to see one of the following three things (depending on your OS):
/Users/yourusername/Library/Application Support/Sublime Text 3/Packages if you're on a MacOS machine
/home/yourusername/.config/sublime-text-3/Packages if you're on a Linux machine
C:\Users\yourusername\AppData\Roaming\Sublime Text 3\Packages if you're on a Windows machine
The parent folder of this folder (i.e. the name above without the
Packages part) is known as the
Data Folder, and it's the place where all of your own personalized versions of everything in Sublime are stored. In all three cases, the location in question is inside your own personal user folder.
This location is not touched when you uninstall the application, nor it is affected if you were to just completely delete
Sublime Text 3.app and then put a new one in it's place.
I'm not surprised that you didn't spot the files there, because Apple goes out of their way to keep the
Library folder hidden, since fiddling around inside of it can conceivable cause problems if you're not careful. Similarly, on Linux systems files that start with a period (like
.config) are also hidden by default, as is the
AppData folder on Windows.
You can always find the folder in Sublime by using the
Browse Packages... menu item, which generally puts you right at the one folder there you're most likely to care about.
If you like, you can also open a regular Finder window, use ⌘+Shift+H to jump it to your home directory, then press ⌘+J or
View > Show View Options and check the box labelled
Show Library Folder.