I was wondering if a distro exists that's keyboard-only friendly. Not terminal only, just kind of minimalist and doesn't use a mouse.
I don't believe that you will find a complete distribution only using the keyboard. There are to much applications that must all follow this condition. But you may consider to use at least a window manager that only uses the keyboard. You will find three of them in the default Raspbian repository. They are xmonad made with Haskel, stumpwm made with Common Lisp and ratpoison. For more details just look at
rpi ~$ apt show xmonad ratpoison stumpwm
The default GUI desktop environment (DE) used in Raspbian, as is the case with all normative GNU/Linux distros, can be replaced with any other DE, and in general they're all available in all distros although there might be some configuration differences (eg., the DE in Raspbian is a customized configuration of LXDE, so using LXDE with Ubuntu will be superficially different). Some of them are probably a bit hefty memory wise to be much fun on most models of Pi, of course.
That said, the use cases for this (mostly: "My mouse broke" and "lost my mouse") seem pretty slim, so there is unlikely to be a project dedicated to this end. If you really, absolutely need to do it, you could look into accessibility and configuration options that might make this workable (eg., using hotkeys to accomplish what a mouse would otherwise be needed for).
See here for an introduction to the distinction between desktop environment and window manager. Stand-alone window managers (ie., those which provide a workable desktop without a DE) are probably your best bet as they tend to be less elaborate and highly configurable; openbox and fvwm are examples (Ingo's answer has some others).
However, it's going to be tedious to configure, especially if you don't have a mouse to use while adapting things, and take a bit of researching DEs/WMs, so if "got a mouse" is any kind of option, you might save yourself a lot of time and hassle.
Keep in mind that GUI applications are usually developed using libraries that are WM/DE agnostic, meaning finding or configuring the WM/DE to not require a mouse won't make any difference to the apps themselves.