An Aesculus californica wants to get big, fast. I'd make sure you really have enough room for it. I'd prefer to see it by itself with a simple ground cover, perhaps Berkeley sedge or Festuca californica. Perhaps a simple planting of Mimulus aurantiacus or a low growing Arctostaphylos.

Hmmmm. Sounds like the plan of keeping it on the small size might be harder work than I thought. I have seen a couple of huge trees, but perhaps mistakenly thought they were a few decades old. I do have the other side of the yard that could handle a large tree. I was hoping to put it in a more prominent place.

I have many growing here on my six acres of native woodland. They will get too big for most city sites,especially as they get water during the summer in your garden, which they do not in their native sites. With summer water they will not go dormant in July as they do here, so they will have a much longer season of growing BIGGER. Al

I guess it isn't a good choice. Why in the world do the "fact sheets" I find on this tree describe it as a "small deciduous tree that grows 15 to 25 ft"

I still like it though. LOL

What sort of planting area would I need to devote to it?

25 feet tall by across is a likely size at 10 to 15 years out, but 15 feet is highly unlikely as an ultimate size. With deep soils they can get up to 30 feet tall by 40 feet across. They are very fast growing from seed.

Thanks for the reality check. Lots of pruning doesn't sound fun.

I think I'll look for something that has interesting form and pale bark that is more appropriate for the site.

You might consider looking at some of the dwarf cultivar forms of Magnolia x soulangeana or M. stellata. Pale bark and interesting form with very showy late winter or early spring bloom. Some of the Acacia species can have pale gray trunks without large size; Acacia cultriformis, A. podalyrifolia come to mind. Check out the listings on line for Acacia species at San Marcos Growers Wholesale Nursery for many more interesting Acacia species.

In the Bay Area foothills these are quite common.
I saw a very nice one utilized as you said you would like to plant one, although Nature probably planted this one.
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This is the other side of that street, a bank with a creek at the bottom.
Those are all small CA buckeyes there on the left side of the photo.
Probably a smattering of poison oak too. They have no leaves now either.
Quite a beautiful weekend.
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This time of year the Buckeye provides its own Christmas decorations. Al