This is a hard question to answer but with experience you can better your odds. I do not slay the fish by any means when I go out but I do manage to pick up a few here and there. I have not been skunked at all this year. Not too bad eh!
The thing that has helped me up my odds is paying attention to what is going on when you are on the water. Where I fish, a south wind over 10 miles an hour can be brutal for boat control. I have been skunked the most times in my life when this type of condition exists. However, a south wind under 10 miles is when I have done my best. Go figure!
A north wind is very easy for boat control but the fish seem to be less than active. I have had okay days with a north wind but the fish seem to bite less aggressive. I am sure this has something to do with the fact that when the wind is out of the north, the temps are cooler. This may shut off the fish.
Wind out of the east and west do not bother me in terms of boat control unless the wind is over 10 miles and hour. I have caught more fish when the wind was out of the west though. I believe this has something to do with the fact that I fish the American side of the St. Clair river. A west wind increases the odds of bait-fish being on my side. That is my theory at least.
Another factor that can make or break a day of fishing is water clarity. A stained to dirty condition can shut off the fish during certain times of the year. I try to avoid fishing when the river clarity is bad but will overlook this especially in the spring. Fish not seeing your bait as well is not as big of an issue when the river is stacked with them.
So how does this help you pick the best fishing day? You have to learn to pick and choose your battles (especially if you are married). The best fishing day for me is whenever I can get out but if I had to choose just one it would be when the wind was out of the south under ten miles an hour on the Saint Clair river in early May. Luckily for me, I can pick more than one day to fish!