What size tank? How large are you looking for? What's your ability to feed multiple times a day?
The truth is that there really aren't many shoaling/schooling fish that can be kept in reef tanks long-term, at least not that will display shoaling behavior in a tank.
Trimma gobies are one option, they're very much on the small size, very expensive, and with a very short lifespan. If you can get a breeding population going that could be one option, but I'm not sure how feasible that is.
Chromis will shoal, but they're used to shoaling in very large groups in the wild, which spreads out their conspecific aggression. In a captive environment with only a handful of fish, the most likely outcome is that the school will systemically harass each other to death, one at a time, until you only have one or two left.
Some firefish and dartfish will congregate together, but I'm not sure that it really qualifies as shoaling. It's more accurate to call what they do hovering together, rather than truly shoaling. And even then, it's very much a case-by-case basis - many of them will not tolerate another of the same species unless you have a larger tank.
Some cardinal fish (banggai, pajama) will also exhibit similar behavior, but as with the dartfish it's less schooling and more hovering together.
Which leads us to anthias, the exact fish you wanted to exclude. They're some of the only fish that will shoal in a reef tank, but they often experience the same problem as chromis - in a captive environment there just aren't enough fish to spread out the aggression, so they end up harassing each other to death. This is especially true with the most robust anthias, the lyretail. But if you want to keep any anthias, you either need the discipline and availability to feed multiple times a day, or you need an autofeeder of some type. I could never successfully keep anthias until I added an autofeeder to my tank.
Honestly, in reef fish the schooling behavior is a response to the presence of predators. When they don't feel externally threatened, they go into foraging mode. So unless you have something to provide that predator response (which I certainly don't recommend), you're not likely to see much schooling behavior, especially in a smaller tank.
