In reply to anthonyh:
If you are wanting to travel through some overseas mountains for a week or more, then I recommend the Pyrenees. These tend to be quieter than the Alps, and feel a bit "wilder." It feels easier to get away from roads and lifts in the Pyrenees than the Alps.
Another option is Norway. There are cheap flights to get there, and if you book tickets early enough then trains are cheap too.
Accommodation and food are expensive, but if you plan to wild camp or stay in the DNT huts, then that is not such a problem. Norway is like Scotland - no restrictions on wild camping, unlike most of the Alps. Norway also has more remote walks and treks than in the Alps or the Pyrenees. The mountains are not so high, but because it is so far north you still get plenty of glaciers if you choose the correct destination.