JJ's last post about visiting Shenzhen is very true, the border crossing at Lo Wu (by train) is pure madness, and begin even before you do the MTR subway transfer @ Kowloon Tong or Hung Hom Station, especially & definitely avoid Saturdays & Sundays.

I'm told that first time leisure visitors (at least here @ PRC NY Consulate) are generally not issued multiple entry visas, just single or doubles - unless you are on business or invited by PRC locals with official stationary.

Consider a day trip to Macau, 55 minutes by hi-speed jetfoil and no visas needed, to see the Las Vegas of the East, we had fun at the Venetian. From there, you can easily cross into China on land, it's less than 15 minutes from downtown/ferry terminal to see another emerging "border" city of high rise building & development. (I'm sure someone else visiting Macau can add to this point)