Grown men don't play with dolls, Endi.
Picture your typical simulation of an expanding universe, a balloon with dots on it. As you pump air into the balloon, it gets bigger and the dots separate just like galaxies do. There is no center to the surface of the balloon, no matter if finite or infinite.
For eternal inflation, picture multiple 'aneurysms' on the surface of this balloon; areas where a smaller sphere starts expanding on the surface of the original balloon. In real space-time these new 'aneurysms' would be separated from the original by an event horizon, but in our balloon analogy they are still connected so that air can be pumped in. As the 'aneurysms' expand, any dots you draw on them will again start to separate like galaxies do, and again, there is no center to the surface of the 'aneurysm', whether finite or infinite.
Actually eternal inflation can have 'aneurysms' on top of 'aneurysms' on top of the original balloon, but space- time is only represented by the surface of the balloons/aneurysms in this analogy.