Lots of places I'd recommend if it weren't for the 9 year old.

With a 9 year old I have no idea. Too big a variable.

Have you asked her where she'd most like to go?

Yep. I either get, "I don't know" or, at a suggestion, "that sounds cool." She thinks a trip around the US in an RV sounds great. Me (since I have to drive), not so much.

She's fairly mature for her age and really loves science, animals and museums.

I should say that part of this is kind of a trip that is ours and ours alone; someplace neither of us has ever been. This doesn't mean I never want to go back to those places, I just want it to be new for both of us. Immediately, this nixes Australia, Fiji, Hawaii, Mexico, Jamaica, Canada and several states.

A few places I've thought about: Ireland, Galapagos, Greece, France, Spain. If it were safer, I'd love to go to Egypt.

Moonie and Andrew, when is the best time to go to Alaska?

For Alaska I favor mid-August as the tourist rush is dying down but things are still in season. But if there is something specific you wish to do that might shift things.

If you want to go full tourist at Denali (which is a marvelous place) do be sure to plan well ahead. Denali National Park is extremely access limited (only one road in and it only goes in a dozen miles of public access).

What he said. And you can even add the Disney angle by going to DLP (I recommend putting that closer to the end of your trip, when she starts needing something familiar).

Concur!

Disney, museums out the ying yang, delicious art, the opportunity to dabble in a foreign language without absolutely losing the ability to communicate

PLUS... For a little alone time, just the 2 of you, how about you own Storybook Land Canal Boat cruise?

Not to mention the appeal of cafes and crepe stands!

I agree with Alex, mid to late August is best. I never got around to finishing it, but you can read my Alaska trip report such as it is here. It at least covers Denali.

Because of my wife's work, we lived in Switzerland last summer with our then 7 and 5 year-olds. Two side trips to Paris. Lots of walks, lots of trains. Lots of cafes. A decent amount of museums. Daily French lessons. We did practically everything in French or German.

I don't know if a European trip is what the doctor ordered for you, but if you do it, I think you'll both have a lot of fun.

I suggest going to the hospital before you die: they may be able to prevent your death (depending on what is wrong).