We are flying into Beijing and cruise out of Tianjin.

You are looking for places with convenient transport in the two places, right?
In BJ, you can stay in Wangfujing Street, where the subway line 1, 5 and many buses pass by. Besides, it’s near to the famous Tian’anmen Square, Qianmen Street and Forbidden City.
In Tianjin, you can stay in near Tianjin Eye, which is near many other attractions and the transport is also convenient.