Gator03 standing by...
For less in-demand tickets you can probably just get a True Blue Membership and either (1) apply for tickets when they open up to members:
http://www.chelseafc.com/tickets-membership/membership.html or (2) buy on the official ticket exchange from ticketholders who can't go to a match:
https://cfcexchange.pvxgateway.com/loginGetting a ticket for Man City those ways is highly unlikely so you'll have to either buy from a ticket tout (scalper) outside the Bridge or you can buy from an online ticket exchange.
Waiting to buy outside the Bridge is risky due to not knowing what you'll have to pay but your worst-case is that you come away empty-handed and watch at a local pub.
Buying through an online ticket exchange (which I've only done once to get a Rangers-Celtic ticket) is potentially very risky because you might pay a lot of money then have the ticket get lost or be dealing with a fraudulent seller. I also believe that it is illegal to resell tickets at marked-up prices in the UK for football matches although they don't really police it. But it means that you'd be without legal recourse if something went wrong.
Of the online sites, viagogo is probably the most reputable and they used to have an official relationship with Chelsea FC. But they only have Suite tickets, which I wouldn't recommend since you wouldn't get the atmosphere:
http://www.viagogo.co.uk/Sports-Tickets/Football/European-Premier-Leagues/Barclays-Premier-League/Chelsea-FC-Tickets/E-1859405I looked at a few sites and livefootballtickets looks pretty good, but really I have no idea if it would come through for you:
http://www.livefootballtickets.com/fixtures/chelsea-v-manchester-city-tickets-english-premier-league.htmlAlso, you might join your local Chelsea Club if you haven't already and ask them for help. They might be able to pull some strings.
Lastly, my order of preference on seating location would be:
1. Shed End (best atmosphere in the stadium and located right next to the away fans)
2. Matthew Harding Stand (pretty good atmosphere)
3. East or West sides ("yard line" tickets, atmosphere is a little lame but for Man City it will be a lot better than usual)