Coming from Obernai I would assume that you be driving up the A65/A61/A63 to Mainz, in which case you can cross the Rhine using the A643 bridge just west of Mainz taking you to Wiesbaden or you can drive along the river to Bingen and use the ferry there. Frankly I'd use the bridge as it doesn't cost anything and the drive from Mainz to Bingen is not that spectacular to make it worthwhile staying on the left bank (it gets more interesting between Bingen and Koblenz, though).