Dia-Compe straddle brake cable?
 

I'm trying to replace this brake cable, but I don't know what to call it when looking for new ones online. See the image. It's a straddle brake cable? It goes to an '80s? Dia-Compe brake set.

No. That's a standard drop-bar brake cable, available anywhere.

Right.

If you're also replacing the outer cable (the housing), be sure to save the whatchamacallit (the thing there in your photo on the end of the housing that clicks into the hole in the brake hood).

We usually call them ferrules. $9 for a bag of 10: http://www.bikeman.com/BR1240.html

We usually remember better when we're less tired.

:)

We also usually save old parts when they're not worn out--especially when they're not easy to replace. This one appears to have a built-in retainer spring, which is handy.