Torsten, It's just what like Mike says, Bro; gotta say where you are going to be. This place is frikkin huge.
If I may - suggest you hang in the East Coast metroplex. I might get a sweet (and much cheaper) hotel on the Maryland shore. Totally convenient to everything but oh, so much more picturesque, and the food !! Crabs, and pone, and oysters, it will turn your North German butt Bavarian.
It's also central to perhaps 99% of what you may wish to see. That region contains those places that define our history. From there, you may easily reach Yorktown, Monmouth, Mannassas, Chancellorsville, Gettysburg, and yes, Spotsylvania, Cold Harbor, Petersburg and Appomatox. An intellectual feast.
For War-II stuff, I might suggest the journey begin at the Smithsonian in DC. After that, there are literally pooploads of places within an hours drive. There's Carlisle Barracks in Pennsylvania (bei Gettysburg) that has a library. And it has librarians, any one of which I would put up against a thousand whining AE soldiers.
And when that's done, it's time to visit Mike in NC, and put it all in context. 'Awadley' kinda has the right of it, because much of the history is captured by the branches and units that took part. US Military bases are indeed open to visitors, and often have interesting stuff that ain't in the official ayllabus. That area was a nexus, but believe me, they will let you in and they will help all they can.
If I may - suggest you screw the stupid big tourist hotels. Better beds, better food, better prices, better ambience, where real people live. Talk to brother Mike. In any case, hope you have a happy visit to my country.
Your friend, John