could also rent a car...
If you don't need to catch the quickest trains (ICEs and ICs), then often the cheapest way to get around is with the Länder tickets (or Schönes -Wochenende-Ticket at the weekend).
http://www.bahn.com/i/view/DEU/en/pr...r-ticket.shtml
http://www.bahn.com/i/view/DEU/en/pr...e-ticket.shtml
They include buses and trams too which is good for city sightseeing.