In principle, it is very simple: move the Documents folder and the Music folder to your Dropbox folder. However, some applications will assume the folders exist in ~/home, so you should create links in your home folder to the "real" folders.

you do that by the command:

ln -s ~/Dropbox/Documents ~/Documents

and

ln -s ~/Dropbox/Music ~/Music

(after you moved the folders to the Dropbox folder)

These links act as if they are actual folders, but the files will be stored in the Dropbox folder.

In my opinion, this would be the most elegant way. There is however a more drastic way to set the default paths to your user's directories:

mousepad ~/.config/user-dirs.dirs

you would see the contents of the file like:

# This file is written by xdg-user-dirs-update

# If you want to change or add directories, just edit the line you're

# interested in. All local changes will be retained on the next run

# Format is XDG_xxx_DIR="$HOME/yyy", where yyy is a shell-escaped

# homedir-relative path, or XDG_xxx_DIR="/yyy", where /yyy is an

# absolute path. No other format is supported.

# 

XDG_DESKTOP_DIR="$HOME/Bureaublad"

XDG_DOWNLOAD_DIR="$HOME/Downloads"

XDG_TEMPLATES_DIR="$HOME/Sjablonen"

XDG_PUBLICSHARE_DIR="$HOME/Openbaar"

XDG_DOCUMENTS_DIR="$HOME/Documenten"

XDG_MUSIC_DIR="$HOME/Muziek"

XDG_PICTURES_DIR="$HOME/Afbeeldingen"

XDG_VIDEOS_DIR="$HOME/Video's"

I would suggest the first option, because it gives you what you describe, without changing default settings.