I thought Neanderthals had greater nutritional requirements than homo sapiens and from what we can gather didn't pass down innovations very well? They also seemed to have lack the ambition/imagination of homo sapiens (I remember watching this docushow talking about how neanderthals lived across this large but passable body of water with a bunch of good land on the other side but never crossed it, whereas under the same conditions homo sapiens did).
Anyways, while the odds seemed stacked that they wouldn't have the foresight to farm nor the desire to give up protein now for grain for a city later, if they did develop agriculture I would imagine it might come from a group developing the same level of agricultural sophistication as some homo sapien hunter-gatherers (this group, growing crops at their temporary hunting grounds, have fed better and thus bred more prodigiously and have passed down the knowledge more from darwinistic principles of self-teaching by watching and copying than from cultural transmission or a civilizational isntitution of agriculture).
Other groups begin following in their path behind them, harvesting any crops the first group had to abandon to move on to the next hunting ground and dropping the seeds. The next group after that moves through, leaving their waste and trash behind, unintentionally fertilizing the ground.
Have this sort of thing happen and you might get an accidental Neanderthal caravan farming civilization? Plus how long before one of these crop-filled campsites is left and is taken over by a group whose able to live in that static spot. They'll develop fortifications to fend off the next band that comes around and voila, you get the first Neanderthal agricultural early civilization stage city.