I don't think the resorts offer transportation to the TTC anymore--but I could be wrong. You could talke a bus from the AKL to the MK, then monorail to the GF from there.
Personally I wouldn't leave the AKL. The GF is pretty, but it's not "drop dead gorgeous" like the AKL. There are so many things to do and see at the AKL you will not be able to do and see them all in one day. DH I walked through the entire hotel looking at hte art collection, I think we missed some of it, and it still took us over four hours. Then there is the firepit, nightvision goggles, animal viewing areas, cocktails in Victoria Falls, the Marketplace, the lobby... You could easily spend several days at the AKL without ever leaving!
Anne