4 days in Germany - need ideas please.

You'll be in a really nice area. Rinteln has some really fine Weserrenaissance buildings. Bückeburg Palace is nearby - pay it a visit.

Hameln (Pied Piper's home) is a nice place to visit near Rinteln. You could drive some of the Fairy Tale Route and the German Timber-Frame Road. There's a TON of old-world Germany to be seen in the smaller towns of the north. Read up to see which places interest you the most. Hannoversch Münden is particularly full of half-timbered buildings.

To the west is the Münsterland, a scenic area with moated castles and windmills on the way to the Netherlands. Münster itself is a nice city as well. Make a stop in Lüdinghausen for a look around.

In the Netherlands, Rick Steves has suggestions for the Arnhem area that are worth looking into.

I've been hearing that people really love Hamburg.

You don't have to drive to Southern Germany to see beautiful places. Believe it or not.
The towns of the Weser Renaissance and the Münsterland to the west of Hannover were already mentioned. Another option are the Harz mountains to the southeast of Hannover. There you can see several perfectly preserved towns with literally thousands of half-timbered houses. Two of them, Goslar and Quedlinburg, are World Heritage Sites, but towns like Wenigerode, Stolberg or Wolfenbüttel are just as nice. Halberstadt offers one of the purest examples of a French Gothic cathedral in Germany, and in several other towns you can see old Romanesque churches.... two in Hildesheim are World Heritage Sites.
The Harz mountains also offer the biggest steam train network of the country. One of the route takes you to the highest peak of Northern Germany, the Brocken.

PS: here is a map with Germanys highlights according to Baedeker, the countrys most popular travel guide:
Highlights of Germany

As you can see, plenty of things to see in the north...

In the Netherlands the Hansa cities along the River IJssel in the east (Hasselt, Kampen, Zwolle, Deventer and Zutphen) make a good stop before venturing to Amsterdam. For good reasons they are brought to attention for those who equal the Netherlands with Amsterdam: look at this website.

Last summer we did a circle around Northern Germany. We loved loved loved Bremen, and Lüneburg. (We also loved Lübeck, Cuxhaven, and Stade but they might be a bit far)

Near Lüneburg is the Lüneburg Heide. Which is a National Park. We stayed on a working farm, and it was so cool! (Hotel Hof Tütsberg)

Near Bremen is Bremerhaven and there is a really great immigration/emigration museum. We were interested in it as the purpose for our trip was to represent the American Branch of the family at a family reunion. (There may or may not have been some tears when I reached the Statue of Liberty part of the museum. So emotional!)

I wish we had more time in Bremen. Bremen was dedicated to "family" things and would have liked to have some time to explore some of the shops. But I rubbed the donkey's hoof on the Bremen Town Musicians - so it means we will go back :)

Cuxhaven is where the Elbe River enters the North Sea. There is a viewing station where a voice tells you about the ships going through the passage. It helps to know German, but to see the ships is really cool. We enjoyed dipping our toes in the North Sea. There is also a cart you can take when the tide is out to some of the outer islands. Or you can walk on the mud flats. We hit it at the wrong time, but still interesting.

I have also heard really great things about Celle, but have not been there.

I would save Southern Germany for another trip.

The Herrenhausen gardens in the suburbs of Hannover are meant to be spectacular.

Note that nobody's mentioned Hannover itself - I got stuck there for an afternoon a couple of years ago and can safely state that it's the dullest major city centre in Germany.

Lot's of good suggestions, and I'll throw in Arnhem and Nijmegen if you have any history buffs in the party (pretty towns also), and Koblenz (if you want to get a bit further south). My brother, who's more familiar with that part of Germany, loves the Deutsches Eck, and it's easy to get to and around even for older folks.