This could have been a good shot had I not forgotten to move the filter round when I turned the camera on it's side. It made me wonder if the grad filter would have been better placed in the bottom half of the shot to darken the cloud or would it have been better off without? Ad astra per aspera
But this picture is actually about the most interesting of questions when shooting outdoors--waiting for light. In this case, the sun is probably going behind the clouds for short time periods--you can tell because there's a big patch of blue. In such a case, you should wait for the light because otherwise the picture is essentially spoiled--because there is not enough (or the wrong kind) light on wall and the flag.
However, if the flag is in the shadow of the building and will be for say, the next six hours, waiting is impossible. In such a situation, you must make do. In my film days, I would bracket the shot with f-stops on either side of my best exposure guess. If you do this digitally, you may have pictures that are easier to manipulate in Photoshop. In this case, I would choose to work with the picture that gave me the best detail of the stone wall.
Another thing you can try is to "change" the background by moving around a bit. There may have been an angle here where the flag is in front of the big white cloud. That may have helped the composition and it might have made it easier to Photoshop. In any case, you give yourself a few more options if you find yourself constrained in other ways (you're in a tour group, your kids are furious that you have stopped again to take a picture, etc. etc.)
But if your goal was to show a blustery cold spring day, you succeeded. I can assure that I have nothing so warm to wear that I would have wanted to wait very long for the light. "Remember the I35W bridge--who needs terrorists when there are Republicans"
I think I took the photo from that angle since that was where the flag was billowing such that I could catch the dragon. Easter monday with 20 tourists in my way and an impatient friend getting cold, as you say constrains the time and composition! Ad astra per aspera
When color came along, hanging a red filter in front of the lens seemed especially pointless. Happily for my father, the polarizing filter had just gone on sale when he made his first serious moves to color. And it works MUCH better than a colored filter anyway--it doesn't do anything about the water in the air, but it does make it possible so the light the humidity is reflecting doesn't show up in your picture.
His nature photography lenses had their own polarizing filters that almost never came off. And you don't CAN turn them "off" if they start causing problems like eliminating the reflections on the surface of water, for example. "Remember the I35W bridge--who needs terrorists when there are Republicans"
I still use red and yellow filters on B&W film: these are the black and white days!
As for making the surface of water disappear--that is a known hazard of polarization. I knew a guy who almost killed himself landing an airplane on a lake--turns out he was breaking in a new pair of polarized flying glasses and the word had not yet spread about some of polarization's drawbacks. With the lens filter, of course, you just rotate the front glass 90° and you are back to the "real" world. "Remember the I35W bridge--who needs terrorists when there are Republicans"
So I have spent some time collecting strategies for getting the best pictures under the circumstance. And of course, the best strategy is to go out with your camera when the light is most likely to be good. Unfortunately, many photogenic sites are closed during golden hour. "Remember the I35W bridge--who needs terrorists when there are Republicans"