The Technik Museum at Sinsheim
If your primary interest is WWII military materiel, this museum has the most of the two Technik museums. In addition to a huge collection of planes, trains, and automobiles, the large military section includes quite a few tanks, planes, uniforms, vehicles, and miscellaneous display cases full of photos and random paraphenalia. The museum is about 20 minutes beyond the Speyer Technik Museum and easily accessible right off the autobahn.
The military section alone takes several hours to thoroughly cover - the display cases are full of photos, personal artifacts, documents, and weapons.  Dioramas depict US, German, and British vehicles and uniforms. Overhead displays include a wonderful intact Junker 52 plane, Messerschmidts, and a Storch obs plane. There's even a V2 rocket found in Siegebach in 1998!
Particularly interesting are two Panther tanks. One IV is unrestored, recovered from Tscherkassy Russian where it was destroyed by its crew in Feb 1944. Another completely restored Panther V Aus G has an operational turret and track - drop in the Euros to watch it work! There are also several Shermans, a Hetzer, and both German and US TD's.
This Stuka JU 87 was recovered - almost in one piece - from 70 meters deep off St. Tropez in Jun 1989. The museum is still searching for more information on this particularly plane, which has been left as it was found.  The Stuka was a two-seater dive-bomber used primarily in the early years of the war.
The museum has at least 3 Russian T34's, widely recognized as the sturdiest and best-designed tank in WWII. Outdoor displays include another T34 and numerous tracked vehicles of more modern vintage. One German commander complained the German Panzers were so finicky compared to the Russian tanks that  they seemed to have been designed by watchmakers!
After you've had enough of Jagdpanthers, a German locomotive used on the Russian front, an extensive Afrika Korp diorama, and multiple displays of US materiel and uniforms, take a look through the well-supplied bookstore. We recommend Brauhaus Jupiter for a delicous and inexpensive lunch, only 600 meters from the museum .