Your previous city remains your home, unless you decide that it is not any more, while the second city becomes your second home. Yes, you can travel between the two cities, provided that you reach the other city before noon time, if the distance between the two cities is more than 44 km's.
Hence, if you left one of them before noon, and reached the other after noon (after Zawal, which is beginning of Zuhr prayer time), you can not fast that day.