Where to stay (and how long) and what to see around Nuremberg

Bamberg and Würzburg are good destinations for day trips. Both some hour away on the train. The kids might love the fortress in Würzburg, across the river. You can walk up through vineyards.
Another kids-friendly destination is Regensburg. There is a boat trip to the Walhalla. The Walhall will be of medium interest, it just being a collection of busts of famous Germans, but the trip could be fun.
The rally grounds are a sorry affair, but that might be the lesson of it all. It's at walking distance from a suburban (S-Bahn) railway station.

The Nazi parade ground is decaying (the concrete and the marble that Speer chose are reacting nastily against each other, so much for the "thousand year reich") but the exhibition in the half-complete assembly hall (Doku-Zentrum) is fascinating. Probably not suitable for kids under ten, though.

Bamberg is fantastic, I strongly recommend that you visit.

Of course there's lots of stuff to do in Nuremberg, including the castle and just wandering around the Altstadt. If the kids get restless with all the history and buildings, other suggestions might include a visit to the Tiergarten (zoo) or the Stadtpark or any of the other lovely parks in or near the city.

Eat some Nürnberger bratwurst and Schäufele for me!

Nürnberg is a good home base; I like the Drei Raben hotel near the hauptbahnhof, but since you're traveling with kids, you might search Wimdu or VRBO for an apartment to rent for the 4-5 days. Bamberg and Rothenburg get my votes for side trips. You can do those things easily by train. Not sure about the Playmobil land.

We took two terrific daytrips from Nuremberg by train, to Bamberg and to Regensburg, each perhaps about an hour each way (?). Connections were easy I do recall. I don't know what young children might make of them, but we thought they were among the loveliest towns we'd seen anywhere. Also nice sized for a pleasant day of strolling. We rely mainly on trains when we are in Europe, but we very much enjoyed a rental car for the days we spent along the Rhine and Mosel. Safe travels.

Here's a link to Playmobil -- http://www.playmobil-funpark.de/en. It's also accessible under the link to Stadtpark in my message above. Just click on Amusement Parks on the right side and it will pop up.