Please comment on your experience with Plantation shutters. Yes they look great,

Shutters will do little to nothing to help I'm afraid. Heavy drapes is an option but if you have the chance attaching something such as ASC sound planks to the window can work wonders. You can use Velcro to attach them so they can be removed to open the window when not needed. I am sure other similar items would work as well. Also consider the Marigo labs tuning dots for a very low profile way to damp the window

I have a double window (two completely seperate isolated panes mounted with a small offset between them to reduce chances of resonance in the window) with shutters in between as well. The inner window then has sound planks (three on one pane, two and a SR ART resonator and HFTs on the other) and also the large (40mm) Marigo dots on each pane

Each part helps but the main conclusion is you can (and probably should) treat a window like any other wall but obviously the end result is not going to win any interior design prizes ...

In a prior installation I lived with acres of glass and light treatment with the SR ART system and while no where near as acoustically well controlled as my current set-up it was very listenable

ps there is a fairly long track record of Marigo dots working well on exposed glass -- it can’t hurt give Ron Heydrich a call he’s a great guy and may have some good ideaas

Mitch's response makes me realize that the shutters could be installed on top of/over the acoustic window treatments I described (sound planks et al), so you could treat the window and have the look your wife is after. As others have noted the shutters themselves are acoustically transparent so there's nothing to stop you treating the surface behind them and getting the look you need. Heavy drapes will actually be very expensive so wonder if you should try something else before you spring for that?