This is a somewhat broad and "open" kind of question.
I lead around 7a on (limestone) sport routes, and have done a basic trad climbing course (placing gear, setting up anchors and some problem solving technics) . Additionally, over the years I've had climbed a few peaks around the world (to elevation of up to 6000m) , in which I've had also followed as second on a nearly vertical ice pitches.
I want to start bringing those things together in the form on alpine climbing, but I'm not sure where to start. I have the option to spend around a month this summer doing so, so I'd love to get some ideas and advices on how.
The first option I currently have in mind is basing myself in Chamonix for a month and just try doing as much as possible, but that could be tricky as I don't have partners, and I don't know anyone around. Would be a shame to get all the way there just to be running around trying to find people.
The second option is going to Squamish, and focus in rock (taking sport-limestone stuff to granite-trad land)
You can start anywhere, to be honest. You don't need to be in the alpine setting to learn how to lead confidently on gear (and....it's probably not even a good idea). Go anywhere there is granite (but other rock types work too) with appropriate-level routes and relatively low commitment. Try different places. Alpine climbing, in its many forms, is not something you can usually work up to in a summer. But that's, like, just my opinion, man.......