I was in Italy last fall (nov) and almost 4 weeks travelling on the crappy Trenitalia from Sicily in the South to Milan/Como in the North.
I liked Milan ... but not for the pics or the shopping... I liked it because it was COLD then and I found the people friendlier than Rome or Naples (but not as friendly as Sicily).
and your gf probably wants to go to the Golden Quad in Milan... but really its no big deal. And I was there the week before christmas too... maybe more interesting if she has S$50k to go shopping

... but really, it is cheaper to shop at Prada in Singapore.
$2k is practically not possible unless you bring your own plain water, and eat the same one block of bread and cheese EVERYWHERE. In short, you will not have fun... and really there isn't much to shoot in the big cities (unless only street photography?).
... I suggest you consider non-eurozone E.Europe ... you can make your money stretch further. And probably have a more unique experience.
7 years ago when I did Eastern Europe for 3 weeks it was possible to spend $2k for everything incl. airtickets. We did Hungary/Croatia/Slovenia/Czech and pass thru slovakia. But these days with Eurozone, not sure if you can. I remember trying to negotiate with customs officials on both sides of the Hungarian/Croat border in the middle of the night ... seeing bullet-ridden houses coming into Split, getting followed thru the roman ruins by Nazi skinheads, followed by a bunch of orthodox grannies in black in Dubrovnik trying to rent us their rooms, browsing the fruit and flower markets at Hvar, thinking how lucky we were to have a room on the ferry to Trieste while the locals slept out on the open deck to save money, running for the ferry at Split only to miss it by a few mins and having everyone on the ferry waving to us ... making friends with an Iranian who was a veteran of the Iran/Iraq war and now lives in Brno, who told me his experiences in the war ...
ah, memories.
If you are young keep W.Europe for when you're older and lazier and rough it out somewhere cheaper that you wouldn't want to do later in life. Besides these just mentioned, consider Turkey... its not too expensive and very unique. Further, I don't know about now ... but E.Europe was safer (less crime) than W.Europe. At least for Italy, I would have to agree vis-a-vis my previous experience in E.Europe.
I abandoned all my SLRs and bought a new Fuji Z2 digicam 2 hours before I got on the plane for Italy. Best thing I ever did! I shot some nice pics and enjoyed myself. You won't have much fun lugging eqpt around... not to mention worrying about theft. I nearly got picked in Rome.