Stick your neck out.

How often do you wear a button down/dress shirt open, showing off a little chest?
It is THE essential for men. One in blue, one in white. Those are key.
It's just as easy to throw on as a tee, but chances are you will get more comments about how nice you look if you wear a collard shirt. Hands down.

Now onto the subject at hand.
When you're wearing a collard shirt and you don't want to go too formal, but you do want to dress it up a bit then try a neckerchief. Not an ascot. Don't get those two confused. An ascot can be very formal, a neckerchief on the other hand can go either way.
Tied simply and worn tucked or falling out of the shirt, Silk or cotton, it is a great addition to a simple outfit and you can go wild with patterns.
I use a classic blue and white bandanna pattern neckerchief more than anything.