Hi August,
I've been considerign what I woudl take myself in a case like that, trying to limit myself to relatively few lenses
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So, the first lenses that came to mind were an UWA, preferably zoom, as for its intended use large apertures wouldn't be a problem, and a large aperture approximately standard lens, for low light shots, so would be not a zoom.
You have covered both of those with the EF-S 10-22 and the Sigma 30 F/1.4. I would have chosen the same UWA zoom, and probably chosen one of the following: EF 28 F/1.8, EF 24 F/1.4 L, EF 35 F/1.4 L. Ok, I own the 28, so probably that one.
For another lens, or maybe two, it depends a bit on what you intend to shoot. If I would stay inside the cities all the time, my first next choice would be the 24-105 F/4 L IS. Great range for all kinds of details (landscape, architecture, markets, etc.) and portraits of all kind and fashion. And the IS adds that extra bit of portability in low light, provided your subjects are relatively still.
I would probably add the 70-200 F/$ L IS as a second lens, sorry, fourth lens, in that case, and bring the extender 1.4X II as well, just for those occasions where you need a little more reach.
Now, if I would actually spend a fair amount of time in the field, the 70-200 RF/4 L IS would be my third choice, because of the slightly compressed landscapes you can shoot with it, and for candid shots, and all kinds of details. The IS again helps in lower light and fairly still subjects.
And the 24-105 would be my fourth lens in that case. See above why.
Two weeks is a bit short, timewise, so I would suggest not to get more lenses than the two mentioned above, plus an extender if need be. I found the 70-200 needs little to no time to get used to, but the 24-105, and probably any lens in that range, does. So I would regard two weeks more or less as the minimum amount of time required to get and get used/test and exchange (if need be) a lens.
Anyway, those would be my choices.
I suddenly realize you don't want to spend a lot of money. Ah, well. In that case the EF 70-300 IS, or one of the EF-S 60 macro or the EF 85 F/1.8. The 60 macro or the 85 instead of the 24-105, and the 70-300 instead of the 70-200.
BTW, I wouldn't visit the Tuscany hills without a ~100 mm equivalent... It is a classic length for slightly compressed landscape shots in a hilly environment. If I really had to limit my choices to just 2 lenses, for Italy I would take a 20 to 24 mm (so the 10-22 zoom is perfect for this) and a 100 mm equivalent (60 macro). I could probably do 95 % of my shots with those two.
HTH, kind regards, Wim