Face, back, or something else? What’s your preference for lathe location and why?
Nice shop bud!Same as Steve - mine is up against the wall due to space considerations. You can see it between the windows in the back of this picture (sorry for it being a bit obstructed).
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I carved out a corner of my single garage space. I face the garage door where the morning light comes in. Tools are conveniently hung on the wall to my left, sharpening station is on the narrow table right behind me, and I can just open the garage door if I need to get to the back side of the lathe to clean up or retrieve something I dropped. It works well for me.Face, back, or something else? What’s your preference for lathe location and why?

Very impressive, that looks like a woodworker's showroom...well done.Same as Steve - mine is up against the wall due to space considerations. You can see it between the windows in the back of this picture (sorry for it being a bit obstructed).
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And an unused one at that!Very impressive, that looks like a woodworker's showroom...well done.
I'm currently facing the wall. It's not that bad since all the tools are on the wall I'm facing and a short reach away. The down side is that my back is to the shop entry and I've had a few people surprise me when I'm in the "turning zone". I'm considering switching to be between the wall and the lathe so I'm facing the entry or placing the lathe perpendicular to the wall.Face, back, or something else? What’s your preference for lathe location and why?

This.As you can see many people layout a turning area where tools and sharpening are readily available. Regardless of whether one faces the wall or window or the shop, think about what needs to be readily available and where it should go, as well as chip cleanup.
I did this paper layout thing for my new shop while I was waiting for construction to finish. After the framing was up, I went and stood where I thought the lathe should go, mimed some tool reaches, sharpening, etc. The first thing I moved in was the lathe. Stood there again to make sure. After that, I placed the next most important machines, one at a time, in order (bandsaws, bench, storage, 2nd lathe, etc). Moved things in one at a time to make sure the important stuff was in the right place without a lot of other stuff getting in the way.Do a physical layout on paper with cutouts of tools etc and move things around, think it through, move things around again, think it through etc, no need to get in hurry with work space layout, it can be a pita to change it all again.