Recommend you tour Heidelberg. We have visited both cities but lived in Heidelberg for over a year in the mid nineties. Heidelberg has a rich history, key sights include; Heidelberg Castle (13th Century), Alte Brucke (Old Bridge with multiple Arches), Old Town, Funicular Railway where u will get interesting views over the Neckar valley, the Rhine valley (pls see link below--railway runs in winter) very old Churchs (St. Peters, Church of the Holy Spirit (built o/a 1236, 1196 respectively). The Christmas Fair (Heidelberger Weihnachtsmarkt)is open from Nov 25 thru Dec 22.

For beer lovers the Heidelberger Brauerei (Brewery) is one of the oldest in Germany (circ 1603)

Hope this helps

Photos of key sights:

http://www.heidelberg-guide.com/gallery_photos.html

Funicular Railway link:
http://www.bergbahn-heidelberg.de/