A good tunic has a bit of weight to it before you even get it on the hanger properly. Pick it up and it should fall rather than crumple, no stiffness in the fabric, no feeling like it will crease the second you sit down. I always give the hem a little tug too. If it springs back into shape, that's a decent sign. If it stays stretched out in your hand, put it back.
This is the thing I reach for on days that don't fit neatly into smart or casual, which is most of them really. Over leggings for a school run, with proper trousers for something that needs a bit more effort, under a coat in that awkward stretch between seasons when a jumper is too much and a t shirt isn't enough. It's not an occasion piece exactly, more a solves a problem piece, and I think that's underrated. The ones with a bit of drape work right through fairly mild winters too, layered under something warmer, so they're not strictly a spring and summer thing even though that's when most of us buy them.
In the shop, check the side seams and the length against your own height before anything else, because tunic lengths vary wildly and what skims one person's hip sits mid thigh on another and looks more like a dress on someone shorter. Have a proper look at the neckline too, some gape the second you lean forward, which you won't notice standing still in front of a mirror but you will notice all day at a desk. And check what happens at the washing instructions. A lot of the softer, floatier fabrics look gorgeous on the rail and then come out of a first wash slightly smaller, slightly bobbled, never quite the same drape again.
Where it falls down for me is anything fitted through the waist or anything that needs real structure, a tunic just won't give you that, it's a looser silhouette by nature and fighting that is a losing battle. I also wouldn't buy one in a very thin or clingy fabric unless you're happy with what it does sitting down, because that's where a lot of them show more than they promise standing up. And if you need something that reads as proper smart, for an interview or anything with a dress code attached, a tunic is nearly always the wrong register, however nice the fabric.
Next time you're looking at one, check the hem first. If it still has body to it on the rail, that's usually a tunic that will still have body to it after a dozen washes.