In reply to Somerville:
As some people have mentioned it's quite tricky to find big walls at that grade in Europe that can't be done in a day. But a couple of other possibilities which might provide the sort of experience you're looking for are:
The North Ridge of the Badile, it can easily be done in a day, so it's not really a great candidate for a proper multi-day climb.
But when we did it the hut was full, so we bivied at the start of the climbing, a little way up the ridge (You just need to ascend a couple of snowfields to get there). There is a small notch just after the snow slopes, with a small stone ledge that can only fit 2-3 people. So although it's not really a multi day climb, you can get the feeling of sleeping on a big wall, as it's a big drop below you and you've got the North Face of the Badile above you with the famous Cassin Route, so it's quite a cool experience.
We also did a multi-day route in Wadi Rum (not in Europe, I know, but it's not a long flight away) that involved completing a route (there are lots of long routes that finish on the summit plateau) and then a bivi on the summit plateau before descending the next day, and that was also quite a special experience.