The choice should be obvious: Bielefeld.
Selling points:
1. It is a natural center of Northern Germany (so Swabia and Bavaria are not necessarily a part of Germany with its capital in Bielefeld; Austria may have them: we don’t really need them all that much anyway). It is on halfway between Rhine and Elbe, halfway between Rhine-Ruhr and Saxonian industrial regions (well, kinda), halfway between Cologne and Berlin. If Netherlands are also part of Germany its central position becomes even more obvious.
2. It is located in Prussian territory (assuming the POD is not before XIX century) but is not associated with Prussian militarism and authoritarianism but neither is it a symbol of constitutionalism and democracy like Frankfurt is. Thus it can be result of compromise between constitutionalists and Prussians (and of course without early PODs Prussia should be major player in unification).
3. It is right in the middle of Teutonburg Forest, so romantic German nationalists of XIX century should be ecstatic (and since nationalism is one of the main driving forces for unification it should matter a great deal).
4. It
doesn’t really exist, so even if enemy would be able to crush TTL Germany in a war, it won’t be able to find and capture its capital and thus the German defeat would not be complete.