If you need to cross the Rhine river then you may take the ferry. For pedestrian prices start at 1 Euro. If you need the ferry urgently outside the timetable then prices start at 20 Euro. There is a bus stop near the ferry landing, but buses are rare. It's line no. 195 to the research center. The bus stop is called "Rheinfaehre".
From Karlsruhe station it takes about 35 minutes by tram S1 to Eggenstein. You need a ticket for 3 zones. If you plan to return in 24 hours then you are better off to by a City ticket for Euro 4.20 or Euro 6.50 (for up to 5 people travelling together). Prices were valid in Dec. 06.
Eggenstein-Leopoldshafen is situated 20 min north of Karlsruhe, not far away from Autobahn 5 (Frankfurt-Basel).
Detailed info Eggenstein
Detailed info Leopoldshafen
Not far from Leopoldshafen there is a ferry across the Rhine River. It is a very comfortable and romantic way to cross this big river. You can see the old trees of the rest of the former river jungle, called Auwald.
Since the two bridges across the Rhine river are fairly jammed at times, it might be a good alternative to use the ferry between Leimersheim (Rheinland-Pfalz) and Leopoldshafen (Baden-Württemberg). It only takes 5 minutes and is not all that expensive - and it sure saves time!
The local tram S1 or S11 from Hochstetten to Ettlingen passes through Eggenstein and Karlsruhe.
It takes only 20 minutes from Eggenstein to the center of Karlsruhe - and you don't even have to change trains!!!
The area around Eggenstein is very flat, so cycling is a pure pleasure here! There are quite a few bicycle paths around and a pretty neat navigation that leads you from one place to the other!