VRN which is the Verbund around Mannheim does have Bahncard discount: https://www.vrn.de/tickets/ticketuebersicht/einzelfahrschein/bc-ticket/index.html
Otherwise, Darmstadt, Heilbronn, Mosbach, Bad Wimpfen, Sinsheim (museum!), Ulm, Freiburg or lake Constance are doable, depending on your...