Say hypathetically that the Milky Way and Andromeda galaxies spiral around each other criss cross in orbit perfectly, what is in the center?

A whole bunch of super-massive black holes.

In about 4 billion years the two galaxies will pass through each other like two handfuls of sand thrown at each other by two beachgoers. The galaxies will then slow and return then start to circle each other, eventually forming a single globular galaxy. The black holes at the centre of each galaxy will first orbit each other then later they will combine into one

The center of gravity (also the center of mass). We can add up all the mass of all the stars and planets in both galaxies and put that mass mathematically in the geometric center of the two galaxies. And that will define the orbits of the two galaxies around the CG/CM.

At their current distance...? We're about 2.2 million light years apart. Andromeda has about 50% more stars (and an estimated 50% more mass) than the Milky Way has.

So, at 2,200,000 light years, the center of mass of our two galaxies is about 880,000 light years out from the center of the Andromeda galaxy, and about 1.32 million light years out from the Milky Way. Aside from a few scattered atoms, maybe a rogue world or two.... there's likely nothing there.