I would also recommend visiting in April, but anytime is OK just to get a sense of the area. Heidelberg always has events going on, many of which are in English
This is a good website, and the tourist office at the main railroad station has much more.
If possible, include a trip over to France, just a bit more than an hour from Heidelberg at its closest point. Alsace is very interesting, and closest to HD is WIssembourg, a small pretty town; Strasbourg, an old well-know historic city is about 1/2 hr. longer.
One thing you also might like, which does not really exist in USA is a "therme" a sort of large spa, swimming pool, sauna area, great for a few hours, even in the evening. There are many in Baden-Wurrtemebrg, my favorite is Miramar in Weinheim, about 1/2 north of HD. Its fun all year long, even in bad weather.