Hard-line traditionalists may wince, but I think a sport coat with no tie is a perfectly acceptable look. A nice one, even. In fact, when going out to a restaurant or bar, I’ll often wear a sport coat with woolen trousers and a nice shirt, but forgo the tie. This kind of ensemble is especially good in areas of the world where a necktie – no matter how casual – is still seen as somewhat of a formal statement (I’m looking at you, Bay Area).
If you decide to go tieless, I recommend at least wearing a pocket square. Not doing so can leave the look a bit unfinished. Something made out of a matte wool or linen will do better than a shiny, wet silk. The latter will have a sheen that may be too distracting when there’s no tie to counterbalance it. You might also want to tamp the square down a bit, so that it’s not sticking up too high into the air. I don’t think pocket squares should ever look too loud, but this may be even more important if you’re just wearing a square alone.
For your shirt, stick to solid light blues, or something like the soft pink that Alan Flusser is seen wearing above. Both are considered more casual than a solid white. For something even more causal still, consider shirts with stripes or checks (such as tattersalls, graph checks, or ginghams). Remember, the bolder the pattern, the more casual the shirt is considered. This kind of combination – a casual shirt and sport coat, worn with a hank, but no tie – will allow you to look sharp, but also well suited to certain casual environments.