If we make Sphere the Sun, and Pluto is in San Francisco, where does Alpha Centauri go?
Alpha Centauri is 4.344 light years away, so at our scale of 1:8.855 million, model Alpha Centauri must be placed 12 times further away than the Moon. Not 12 times further away than our model of the Moon in Las Vegas; 12 times further away than the actual Moon. Even if we decide to build a model of Alpha Centauri A which is 1.2 times the radius of Sphere itself, it’s going to be a little tricky to make it stay in place.
Fortunately this contemplation of astronomical distances suggests its own solution. Our model of the Earth will be nearly 5 feet in diameter, enough to portray the continents and oceans in fairly rich detail. Obviously this model will require an arrow pointing at south Las Vegas reading “YOU ARE HERE”, with another arrow pointing 1/16 in away reading “SUN”. We can then also mark the locations of our models bodies from Jupiter to Sedna similarly, in model California and model Oregon. With this done, it is a small extension of our model-within-a-model to put Alpha Centauri 1719 feet away from our Earth model, saying “we didn’t include Alpha Centauri in our model, but here it is in our model-within-a-model”.
We can even extend this to, say, the galactic core, 1956 miles away in our model-model. However the Andromeda Galaxy would need to be most of the way to the Moon at 190,000 miles; for this we would have to resort to a model-model-model.
In conclusion: Space, is big. Really big. You just won’t believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it’s a long way down the road to the chemist, but that’s just peanuts to space.
Thanks to John Cody for inspiring this thought!
Picture credit: Skatebiker, Wikimedia Commons
Minds aren't magic 
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There’s a model solar system in Australia (spread out over a few miles IIRC), which has Alpha Centauri seemingly the same kind of distance away as a regular planet, but with a plaque noting that this is in fact the correct distance *assuming you walked to it the long way around the Earth*, because the scale turned out just right for that. I really like that.