An arboretum or other such indoor facility would make sense. Indeed the refit Enterprise and Enterprise-D had one.
As far as windows goes, I think they're an out-of-universe addition to give at least some sense of scale to the viewer of the starship.
In universe, a few observation windows make sense. A place for crew to hang out when there is something to see outside the ship. Otherwise, on a starship spending most of its time in deep space, there isn't going to be much to see outside a window except black. Whether we like the "submarine feel" or not, that's essentially what a starship in space is.
I could imagine quarters having some kind of window-like viewscreen on a wall that showed incredibly realistic (think 3D and HD-like) landscapes and such (like views out a window, including weather changes and the progression of a day). Sound effects could even be produced (wind, rain, birds).
Or, much like today's webcams, a crewmember could call up a realtime shot of an area. Like looking out a window on a view of San Francisco or Paris or any place else.
But windows? More windows? Probably don't need many or any old-fashioned windows on a real starship.
