In reply to Bluebird:
Well that is quite a wide question!
One obvious option after (or for that matter before, as it is not glaciated), the Weissmies is the Laginhorn (in fact the Weissmies is not a glacial route if approached from Almagelleralp). Equally for a worthwhile, but straightforward 4000m peak, the Grand Paradiso is worth looking at, for preference NOT by the very crowded Voie Normalle.
Presumably, however, you are not looking for a list of routes in ascending order from easy to much more serious. Nothing wrong with Cyberpunk's advice, obviously you need to know (and practice), standard stuff like crevasse rescue. You have to get the overall feel of the Alps, their size and seriousness and how conditions and weather can change and how suddenly very frightening things can seem, also how things like huts and cable cars tick.
The best way almost certainly would be to go out for one season with modest objectives in terms of seriousness and escapability. If you can persuade more experienced Alpinists to take you along and help you that can be good (being a pretty girl might help with this, but is probably not anything one can alter), if you are certain that they ARE as experienced and sensible as they claim .
It is also very important to be aware how debilitating altitude can be if you get to it too fast. Above all, never be afraid to turn back on an Alpine route - the mountain will always be there next year, the trick is to make sure that you are (the exception to this is where you are on a committing route - then you HAVE to finish no matter what, which is why it is so serious. But that really is a more advanced stage of Alpinism).
Don't get obsessed by particular routes or tick lists (which is not at all the same as not having objectives), if something is not realistic for whatever reason, find something else worthwhile to do rather than sitting around moping - so that from every Alpine trip you come back with an achievement, even if it wasn't the one you wanted.
Post edited at 17:22