The files would by default go to /var/cache/apt/archives and Filebox or Hamster would be able to fetch them from there for you (not the stock File Manager though). However, to run apt-get you would already be in xterm so it might be easier to just use cp or mv.

Also, apt-get allows to specify an arbitrary directory as the download destination, so you can do it in a single step. The magic option is -o dir::cache=/bla/bla/bla, where the blbablabla could be e.g. /home/MyDocs/Downloads (you may need to create that directory first).