As usual, you'll find a tip in which I recommend to explore the destination by foot. So, here it is: Walking through Heidelberg's old town will give you a first overview over the sights and also provide you with many interesting views. A good starting point is the shopping centre Kaufhof just behind the new Neckar Bridge. From there, enter the Hauptstraße pedestrian zone and follow it (or its neighbouring streets) towards the Heiliggeistkirche (Church of the Holy Spirit). This walk will take you about 20-30 minutes. You can prolong it by walking up Castle Hill.
Who ever was mad enough to put a teeter totter in plain view of unsuspecting adults ostensibly deep in philosophic thought should be kept with the rest of the hatters. This contraption beckoned us until we were powerless to resist. It was no mere up and down teeter totter, but one with a spring on top that caused angles, circles and twists found in no geometry book. It was several hours later (and into the next day) that we realized we had used muscles that had not been tested in years.
I found it fascinating that this is how they sold liquor. There were all types of liquors-whiskey, scotch, cider, etc. People brought their own bottles went to these big glass vats and filled them up.
Walking is always the best way to discover a city. In Heidelberg, the walk from the modern district to the old town can be very pleasant, especially of you are walking on the north bank of the Neckar. It gives a very nice sight of the old town as it gets closer.
The Heidelberg Tourist Office puts on tours of the old town that take you to all points of interest in about two hours. If this sounds interesting, then between April - October the tours start at 2pm on the Universitätsplatz on Fridays and Saturdays and the rest of the year the tours are only on Saturdays. Just turn up and pay - prices are reasonable, less than 20 DM at last check.
Pick up a map, cost €1, from the tourist info office next to the station. An easy to follow walk through all of the cities interesting areas. Took us a couple of hours or so but, it does pass some interesting restaurants and pubs too, see tips later!
It is a nice walk down either side of the river with a number of cafe's to sit a watch the water flow by. There are also a few spots where you can get a boat ride down the river.
From the castle its worth the walk to cross the bridge and see Heilelberg from there. Nice walkway along the river