From Heidelberg, there are several ways of getting there, but the easiest one is a bus that picks up once per hour (on Sundays - probably more often on other days) at the bus stop on the west side of the Hauptbahnhof. However, beware the bus driver. It was only a 20-30 minute ride, but I've never felt so motion-sick in my life. Unfortunately it was the same driver on the way back, too!
Schwetzingen has a couple of main attractions: its castle and the castle garden, and its asparagus - especially at this time of year. There was even a sculpture commemorating asparagus in the plaza near the castle, as well as several market stands selling various produce, but mostly asparagus. Little signs everywhere advertised fresh asparagus. Spargelzeit (aspargus season) is at its height right now.
We spent a couple of hours wandering around the castle gardens, which are really extensive. We hadn't heard much about the inside of the castle itself so we skipped that. Admission just to the gardens was 4 EUR each - although I never saw anyone check a ticket and I think we could have just walked right in! The gardens include a bathhouse (you must wear slippers to go in), a myriad of fountains and ponds, fake Roman ruins, and a little mosque. I don't think we even saw it all in two hours. The weather wavered between sunny and actually raining - but I was glad it wasn't as hot as the last few days. (I'm a wuss in the heat.) Check out the photos below!