TIM Italia is one of the main providers for phone SIM cards so perhaps they have what you need.

http://www.tim.it/home

"3" Mobile Italy is great, they sell a 3gig data card for 8 Euro, no strings attached except that they have to scan your passport. It doesn't work until 24 hours after you buy it and you need to keep the bigger "credit card sized" plastic card that you twist the tiny SIM out of because upon it is your pin code to unlock your SIM. Works a charm with brilliant coverage (excluding while inside railway tunnels and while in Venice). It's really easy to insert the SIM, just use your metal-poker that came with the iPad to remove the SIM tray, place the SIM in the tray, then click it back in.

Irish, where did you buy the sim and data card from "3"? The english website doesn't work for me, and I cannot seem to find it on the Italian site?

I bought mine in Florence near the Duomo, there was also a shop in Rome that I went past, so there is most likely to be one in Milan...I too didn't know where on earth the shop was before walking past it. It seems pretty common, so I'd just look in the main shopping area first. Train stations don't really have mobile providers within in Italy and I couldn't locate the one in Rome Airport, it's just one of those things. According to the Italian website treitalia, there is a "tre" or "3" shop right next to the duomo in Milan on Via Torino. There is an alternative shop round the corner heading into Piazza Dei Mercanti. So yeah, either of those shops should work...

Here's the link: http://www.tre.it/assistenza/negozi-3/negozi-e-centri-assistenza

To find the shops select Lombardia as your region, then choose Milano, followed by Milano. Then just zoom the map in until you are in central Milan.

>>>Train stations don't really have mobile providers within in Italy <<<<

Actually, they do. Termini has several including TIM (upstairs)as does Milan Centrale (TIM, Wind, etc.) and a TIM just outside the station in Florence.

FLAGSHIP STORE FIRENZE1 S.R.L. PIAZZA DELLA STAZIONE 60/61 FIRENZE
Tel.:055285630 Fax:

http://www.tim.it/trova-negozio?se=1&prov=FI%2CFIRENZE&comune=&viapiazza=&cap=&nt=on&nat=on

Store locator.
http://www.tim.it/trova-negozio?se=1&prov=&comune=&viapiazza=&cap=&nt=on&nat=on

I like the 3 gigs data for 8 euro idea. It seems too good to be true, as we pay $35 for half a gig in our part of the world, and that's on a mobile plan. We have a mobile hotspot device, no cell phone, just data, so we were hoping we can get a data sim in Italy. We have not seen one before with just data, no phone number attached, such as what OP would be needing for an iPad.
Thanks for the info kybourbon, I will check that out.