From the Hauptbahnhof, 3km west of the Schloss, there are up to three services per hour to/from Frankfurt (€19.90 to €29.90, one to 1½ hours) and Stuttgart (€23.90 to €39.90, 40 minutes to one hour), as well as S-Bahn services to Mannheim (€5.80, 30 minutes, two per hour) and Speyer (€10.90, 50 minutes, every 30 minutes). From Mannheim you can connect to German Wine Route towns.
The fastest way to reach Frankfurt airport is the Lufthansa Airport Shuttle. It runs every 90 minutes; journey time is one hour.
To get to Frankfurt-Hahn airport, you can take the Hahn Express (2¼ hours, five daily), which stops at the Hauptbahnhof.