For European (Asian too, for that matter) destinations I'm familiar with, I always prefer to arrive during the early mornings, if at all possible.

For whatever reason, I've never needed much sleep and much prefer to hit the ground running, whether it's for business or leisure. There are some hotels I frequent where I've often been accommodated with very early check in, at or around 9 am; but, of course, realize this would be the exception rather than the rule. Otherwise, I'll just have a cup of coffee at the restaurant or find a local one and do some work or reply to emails (I hate emails but when bored enough will reply to some) after dropping off my luggage with the hotel.

For destinations I'm not familiar with or my first time visiting, I'll aim for afternoon arrivals, since I'd rather avoid wandering into the wrong area and risk getting robbed or mugged.