Find files that are not in .gitignore

git provides git-check-ignore to check whether a file is excluded by .gitignore.

So you could use:

find . -type f -not -path './node_modules*' \
       -a -not -path '*.git*'               \
       -a -not -path './coverage*'          \
       -a -not -path './bower_components*'  \
       -a -not -name '*~'                   \
       -exec sh -c '
         for f do
           git check-ignore -q "$f" ||
           printf '%s\n' "$f"
         done
       ' find-sh {} +

Note that you would pay big cost for this because the check was performed for each file.

there is a git command for doing exactly this: e.g.

my_git_repo % git grep --line-number TODO                                                                                         
desktop/includes/controllers/user_applications.sh:126:  # TODO try running this without sudo
desktop/includes/controllers/web_tools.sh:52:   TODO: detail the actual steps here:
desktop/includes/controllers/web_tools.sh:57:   TODO: check if, at this point, the menurc file exists. i.e. it  was created

As you stated, it will do a basic grep will most of the normal grep options, but it will not search .git or any of the files or folders in your .gitignore file.
For more details, see man git-grep

Submodules:

If you have other git repos inside this git repo, (they should be in submodules) then you can use the flag --recurse-submodules to search in the submodules as well

To show files that are in your checkout and that are tracked by Git, use

$ git ls-files

This command has a number of options for showing, e.g. cached files, untracked files, modified files, ignored files etc. See git ls-files --help.