Where can I find hard soled baby shoes size 2?

You can pretty much find hard soled baby shoes just about anywhere. Stride Rite usually have a good selection of hard sole baby shoes. They are slightly expensive, but is worth every penny. They have baby shoes, toddler shoes and youth shoes for both girls and boys. I didn't see any on their online site, but you can either call their customer service line at 1-800-299-6575 Monday - Friday from 8am to 5pm or take a visit at their local store nearest you. I found a large selection of Stride Rite brand shoes at Shoebuy site as well. You can find Stride Rite shoes at department stores like JCPenny, Sears and Macy's. You also might get lucky on the Amazon site. 

When looking for baby shoes, it's easy to get caught up with all the cute soft-soled shoes, like Robeez or Pedi-peds, for new walkers.  However, you can find lots of cute shoes for boys and girls in a size 2.  One of the best sites for shoes is Zappos.  Zappos offers free shipping AND free returns, which is perfect when you need to try shoes on little feet around a nap schedule!
Another site with great deals on shoes is 6pm.  They always have good deals and discounts!