I've decided to augment the correct use of an umbrella, in rainy weather, with some sort of hat. I'm not going to wear a fedora, nor anything that looks too-outdoorsy...when I go hiking, I use my own gear, which is not, IMO, appropriate gear for a city.
Also, I need some non-athletic shoes or boots that I can wear with casual wear, like sportcoat/slacks/overcoat. Not sure about just getting regular athletic-shoe types in black or brown uppers, even though I have a source for those i certainly could procure and would be OK from a distance.
The only criterion for the latter is that they can be worn for 6-7 miles a day, just through the city, even with wool socks, without getting blisters, like my regular dress shoes.
I still will never understand how detectives/cops in the movie go on these epic foot-chases wearing wingtips and shit.