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You can install Cygwin into C:\ actually, which makes / == C:\. I find that does make it feel much better integrated with Windows. And there are several alternatives to the default console: mintty and rxvt if you don't want to run an X server, and xterm and rxvt-unicode if you do.
Have a look at mintty as well. http://mintty.googlecode.com.
The shells are fine; it's the Windows console window that's the problem. I think both projects use it by default to ensure compatibility with programs that use the low-level console API. Sadly, there's no official or straightforward way for intercepting output from such apps.
There is an API for accessing a console's screen buffer, which the Console2 project uses to put a better UI on the console. That approach still has to rely on the console's substandard terminal emulation though.
(Btw, you should see MS's "Subsystem for Unix Application" for a truly atrocious default config. It doesn't even have command line navigation with the arrow keys.)
Mintty is actually based on PuTTY's terminal emulation and Windows frontend parts, but it's tailored specifically for Cygwin. This results in smaller size and a simpler UI.
It also improves on PuTTY's terminal emulation in various ways, in order to make it more xterm-compatible. For example, it supports xterm keycodes for modifier key combinations such as Ctrl+Arrow.
There are also a few additional features such as mousewheel scrolling in 'less', window transparency, and the ability to place the command line cursor with a mouse click.
Mintty can be used for remote connections too, by simply running the likes of 'ssh' or 'telnet' inside it.