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I read on this question What is in the space between neurons in a brain? that there is actually not much empty space in a brain. But my question is slightly different. Is there a visual demonstration I can see of approximately how "packed full of cells" the brain actually is?

Obviously there wouldn't be a fixed answer as it is likely a continuum where the bigger you get the harder it is to swim through without being blocked by all the neurons/synapses. But what is a good ballpark size to be to swim through with relative ease?

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Is there a visual demonstration I can see of approximately 
how "packed full of cells" the brain actually is?

Yes. You can inject tracers in the CSF (Cerebrospinal fluid) or in the ventricles and monitor them. In this study, the authors have injected a fluorescent tracer in the CSF and used a direct imaging.

We used in vivo two-photon imaging to compare CSF influx into the cortex of awake, anesthetized, and sleeping mice. The fluorescent tracers were infused into the subarachnoid CSF via a cannula implanted in the cisterna magna for real-time assessment of CSF tracer movement.

You can also inject a radiolabeled tracer. The tracer should be a molecule that is not taken up by the cells. You can then visualize the space using Positron Emission Tomography (PET).

 But what is a good ballpark size to be to swim through with relative ease?

You may find this interesting: the abovementioned study shows that the "space" expands during sleep and CSF percolates deeper into the brain. This allows clearing of toxic metabolites. Having said that, some interior regions would be difficult to reach. Apart from neurons, there are several glia which occupy the space. I am not entirely sure about this but in interior regions there would be very less of extracellular space (I am just guessing it would be less than ~1µm. See the black regions in the figure below). Extracellular space is 20% of total brain tissue but it is not constant throughout. For more details refer to this book.

enter image description here

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  • $\begingroup$ I wonder if you could repeat that experiment using labeled nanoparticles of known size, as they get larger they'd eventually stop moving throughout the whole space. But if that image is accurate, the space between the membranes doesn't look much thicker than the membranes themselves. $\endgroup$
    – user137
    Commented Nov 12, 2014 at 15:01
  • $\begingroup$ This is a SEM image from the book (that is linked). In the figure captions it is mentioned that "The scale bar is 1µm" but I am not able to find it. The ECS is as you can notice non-uniform (but certainly thicker than membrane in most places) :P That injection experiment can certainly be repeated with nanoparticles (perhaps some kind of traceable ones like quantum dots). $\endgroup$
    – WYSIWYG
    Commented Nov 12, 2014 at 16:08

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