[annapurna]

For that matter, you also have the choice to book a flight into or out of a hub airport like Frankfurt and using the train or a separate airline ticket on a hopper airline like Germanwings to get between the hub city and where you'll be getting surgery.

First, if you have any level of status with an airline, I'd work with their route map on their website. Even if you have mid-level status, you can often get better service than the run of the mill passenger if you use your status. Looking at their rout map will give you an idea of the possible routes and playing around with dates and locations on their website should give you the likeliest lowest cost dates and routes. At that point, you'll almost have to call if you want to have economy out and first/business on the return. If you don't do your homework first, though, most of the time they'll check one set of flights, give you a cost and try to get you off the phone quickly. If you've done your homework or are elite status, they typically work with you a bit more.

If you don't have status with any airline, I'd imagine that Expedia might give you a broad selection of what might be possible but you'd likely need to do a little research beyond them. Condor and Open Skies are options to get to/from Europe that don't tend to show up on a lot of searches. Iceland Air offers a sit-upright first class but also allows you to break up the flights with overnights in Iceland; an idea if your sitting tolerance is good but you simply can't travel for the 8 to 10 hours straight it takes to get across the water.