Theres some quite big threads on this if you search, which is advised. We are not sure why its number 17, but we do know there are City 1,2,3's etc from the board in the 'trainstation' bink video, City 17 must have some significance, such as the first city to be taken over, or the current one the combines are taking under control, or possibly just the site of a rebellion. We just don't know for sure
Well its going along with the whole Totalitarian leadership type feeling of numbered cities like Stalag 41. Also City 17 is where the Administrator/Dr.Breen has established his leadership as he says in the Bink video "I thought so much of City 17 to establish my administartion here." I think the Gman has placed you in City 17 to help him beat the Combine to achieve his ultimate goal, what that is we will learn in the end of HL2, Gabe has said that you will learn much more of the Gman's motives in HL2. I think he has chosen Gordon because he can carry out the Gman's wishes to the fullest, Gordon is the best of the best you might say not only is he extremely intelligent but he is an extremely effective killing machine when stacked asgainst Marines, aliens, and trans dimensional creatures. At least that's what i think about the reasons behind the whole purpose of Gordon being in City 17.
not secret, just unnamed..... they are named by distance..
say you made a city 17KM from vladivostok (the closest major city), in russia, the city would be named City 17.... (if noone had a name for it, like a military town)