In order to hack on a piece of software, you should not use the binary distribution, but the source distribution. For packages in Ubuntu, you can use
apt-get source packagename. For instance, in order to get the source code for GEdit, you'll do
apt-get source gedit. For PPAs that might not work, but you'll get the source from their Launchpad.net page.
You shouldn't really care too much about individual files that comes with a package, because that's what the package system is for, but if you do want to list all the files that were installed with a package, you can use
dpkg -L packagename. In your case, that should be
dpkg -L brackets.
None of those commands require root permissions, so you should not prefix them with sudo.