Well, depends on the look you want, as well as the functionality you are after. If that was my space and I wanted the treatments to be able to be opened and closed easily and at various times of day, I would say two large panels on a traverse rod. I had that in my former living room and now in my family room. If I wanted to treat each window individually, I would either inside mount roman shades (if you have the depth on the inside), or outside mount close to the crown molding.

You need to first decide what you are trying to accomplish with the window treatments. If the mini blinds were gone, would you need privacy or light control from the new window coverings? Are you willing to keep the current blinds and add panels? Stationary panels on the sides would look fine, in my opinion.

It helps to know what style of furniture you have in the room. That should affect what you choose for the windows.

Thanks to you both. The furniture in the room right now is from our old formal LR during my brief French Country phase, probably will be replaced in a year or 2, maybe with a leather couch but definitely more casual. The WT really need to just be decorative- I find I always keep the blinds up and I'm not opposed to taking them down. I don't want anything too fussy. In my old house I had all panels but just worry about all that space above the 4 windows with nothing but a rod!

What about tailored valances over linen pull-down shades running within each window? That way you can adjust each individually depending on lighting needs.
Edie

You can mount a long rod near the ceiling with dummy side panels on the outside, then outside mount wooden shades butted together near the rod to fill in the gap between the window top and the rod.

[Mediterranean Bedroom[(https://www.houzz.com/photos/mediterranean-bedroom-ideas-phbr1-bp~t_715~s_2109) by San Francisco Interior Designers & Decorators Tucker & Marks

[Contemporary Bedroom[(https://www.houzz.com/photos/contemporary-bedroom-ideas-phbr1-bp~t_715~s_2103)

Or you can mount a single valance across the entire 4 windows, covering the window tops and then hide inside mount blinds/duettes underneath so only the valance would be visible during the day. (This valance may not be your style or color, but just to give you the idea.)

[Traditional Dining Room[(https://www.houzz.com/photos/traditional-dining-room-ideas-phbr1-bp~t_722~s_2107) by Northborough Window Treatments KH Window Fashions, Inc.

If you want to look for more window treatment ideas, ther is an old thread on it, linked below.

Here is a link that might be useful: Window treatment ideas

Another example

[Traditional Living Room[(https://www.houzz.com/photos/traditional-living-room-ideas-phbr1-bp~t_718~s_2107) by South Hamilton Interior Designers & Decorators SLC Interiors

I love your suggestions, Annie! (except for the valance). The treatments you show add such a warm, finished feel to the rooms and also seem to cover all bases: function well for privacy or view, classy and they cleverly conceal the lack of a window frame.

Wow! Annie, the panel/blind look is perfect. I get the panels I love but also something to fill in the top. I wonder if I could do as in the second picture-patterned roman shades and then a solid neutral panel? Or if the patterned roman shades would be too much since it would cover so much space?

You certainly can do a pattern, but don't let it go too bold.