OK, here goes on suggestions.
Crop: I'd crop on the right at the vertical line in the stones on the upright just to the right of where the parapet ends. I'd also crop a little on the bottom so that the angled dark line of the step just below the woman actually runs out at the right lower corner. I might also take a little off the left and top but the right and bottom are the 2 crops I would make first, followed perhaps by a bit of a crop at the top to produce a more wide screen image format, much wider than it is tall.
As far as the rain goes, it's hard to make rain itself visible but you can intensify the feel of it by making distant objects less clear so I'd reduce clarity slightly and lift the shadows of the background part of the scene above the top of the parapet so that central background area went lighter and greyer in tone, and a little less sharp. I'd also play with reducing sharpness there a bit. On the other hand I'd try to bring out a bit more detail in the woman's figure, the statue, and the area below the top of the parapet.
The other thing that lightening the tone of the background and opening up the foreground and figure will do is to increase the sense of front to back depth in the scene. It's possible to also intensify those depth cues by using graduated filters and you could use several, brushing out the areas you don't want them to affect. If you're using the CC version of Lightroom, you could also play with negative Dehaze amounts on that background and perhaps a bit of positive Dehaze on the figure and foreground.
It's a nice photo. I think you could do a fair bit with it. It's also possible that it might work better in colour because I don't think there's enough tonal difference between the figure and the roadway and parapet immediately behind her. It's going to be hard getting a tonal difference there in black and white but, depending on the colour of her clothing and umbrella, you may do better in colour if you're prepared to play around a little with desaturating the background slightly while leaving the as shot saturation alone for the woman and that immediate foreground.
If you use Lightroom, you can also play around with doing a black and white conversion by simply desaturating all of the 8 colour channels in the HSL panel. If you convert to black and white that way you'll find that the white balance, vibrance, and saturation sliders in the Basic panel and the saturation slider in the local adjustment options (brush, graduated filter, radial filter) will still have an effect plus you can adjust the relative darkness/lightness of the different colours by using the luminance sliders in the HSL panel. There's several ways of doing a black and white conversion in Lightroom and your editing options vary a little depending on which conversion option you choose.
