Where are the default packages in Sublime Text 3 on Ubuntu?
If you want the easiest way to save your customized settings first copy all the default settings and paste into a new file named Preferences.sublime-settings.
Then make your changes and save the file to:
/home/**username**/.config/sublime-text-3/Packages/User
In order to see the .config folder you will have to enable show hidden files.
The instructions are written at the top of the default settings list in case you are wondering where got this from.
To amplify on @skuroda's answer - ST3 contains all of its data that, in ST2, was stored in Packages/PackageName, in PackageName.sublime-package files that are basically just zip files, or "Resources" as they're now known. Using PackageResourceViewer, you can easily edit the individual files contained within the resource, then save it back again. When saved, the proper directory structure under Packages/PackageName will be created, allowing you to edit the file directly next time. The way file precedence works in Sublime, any file that exists in ~/.config/sublime-text-3/Packages/PackageName/ will override any file of the same name stored in PackageName.sublime-package.
However, since you don't want these files to be accidentally overwritten, I would suggest creating ~/config/sublime-text-3/Packages/User/Themes/ and User/Color Schemes directories and storing your customized files there instead. The User/ directory is protected from overwrites during upgrades, etc., and unless you're planning on creating a customized theme or color scheme for redistribution through Package Control, it's best practice to keep your files in there.
EDIT
I just realized you hadn't gotten an answer to your original question - where are the files stored? If you installed the .deb file from sublimetext.com, all the .sublime-package files are in /opt/sublime_text/Packages.
You can use
dpkg -L <package name>
For example
dpkg -L subli<tab>
In the ST console, try entering sublime.executable_path(). This should get you close to where you need to be. Also, you should copy the content of the file out and move them (under a new name to the packages folder). You probably don't want your modifications to be reverted on subsequent update. An alternative method is to try overriding the files you need to. I haven't done that for theme files, so I'm unsure if everything will work as it should. If you take the override route, I'd recommend using PackageResourceViewer. I wrote it to help with browsing/overriding package files in ST3.