I know routing changes require a reissue and charge, but is this the case when the fare calculation contains cities rather than airports? I picked up my DONE4 yesterday ( ^ ) and noticed it says TYO instead of NRT, CHI instead of ORD, and LON instead of LHR/LGW. Does this mean I can (where/if possible) change my flights to go to/from different airports in those cities for no charge?

Yes no problem.

In fact even if the coupon says, for example JFK you can reroute to EWR or LGA for no charge since these are what is known as "co-terminals".

However, if you think you might want to do this then it does minimise potential questions from check-in staff if you get the coupons issued with the city code rather than a specific airport. Of course in some cases the city code is the same as one of the airports - e.g. SFO or LAX - and in that case you have to just hope it isn't a problem. In the past I have had no difficulty, for example, using a coupon that was originally for a specific SFO-ORD flight on a SJC-ORD, and similarly LHR-JFK on a LHR-EWR, and LHR-IAD on a LHR-BWI.

As christep mentioned, co-terminals are accepted 99.99% of the time without a reissue, so having the city codes instead of airport on the ticket is mostly irrelevant. Personally I've never had a co-terminal mis-processed; agents are used to this (unlike RTW tickets).

Tax levels can vary from airport to airport - particularly LGW and LHR - so if someone is doing their job by the book, they should charge you the appropriate levels (and refund where necessary).

In practice, this rarely happens unless you make a change to your booking that requires a reissue, such as a re-route.

I believe you aren't entitled to a refund, although I don't know the rules well enough to be sure of that. I think I do remember that if you've bought an extra segment and later delete it, you do not get the money back - that's different from taxes, of course. AA has add-collected taxes at a couple of stations, and the MCO of course says "you ain't ever gonna see this money again" or words to that effect.

And on the OP topic of co-terminals, for those who don't read and memorize everything written here, AA does/did not consider the airports in the LA basin as co-terminals. I tried to move a LAX departure to ONT and they wouldn't do it without a reissue. "Yep, they're co-terminals for ordinary tickets, but not for ONE," they said. That was about two years ago, and the ruling was delivered by one of the senior folks on their rtw desk.

out of curiosity - what is the tax savings for a transit and stopover into lgw as compared with lhr?

Contrary to my previous belief, the British Air Passenger Duty is the same for all British airports. It's often mentioned here that "Heathrow" departure taxes can be very high; at least the APD portion is the same at LGW. I don't know if BAA adds their own hit on top of the government's - their web site is awful. The APD is described here in great detail:
http://customs.hmrc.gov.uk/channelsP...505#P200_11988

Interestingly, there's an example in which a pax leaves UK for Paris in coach, connects there to a J seat to the U.S., and is thus liable for the GBP40 departure tax out of the UK.

LGW is about $10 less than LHR.

As a side note, I was not permitted to switch between LHR and LGW flights on an AA oneworld award.

AA OW awards do not recognize co-terminals (or do not allow switching between co-terminals) -- which is quite relevant to this AA award, but not applicable to any other AA usage of co-terminals.