Is there any recommended way to inspect/plot the numeric values that are being sent through the ports between drake systems in real-time?. (something similar to rqt_plot in ROS). Apart from the SignalLogger or writing and wiring custom individual plotting Systems, is there any method to access the port values internally?
There's nothing as nice as rqt_plot as far as I know.
If you are able to alter your Diagram before calling DiagramBuilder::Build, you could add an LcmScopeSystem onto any vector-valued output port and then the port's contents will be transmitted on an LCM channel. You can add multiple scopes, but you currently have to add them one by one, ahead of time.
Once the data is onto an LCM channel, then you could use the provided drake-lcm-spy program which has the ability to show (very rudimentary) live plots:
cd drake
bazel build //lcmtypes:drake-lcm-spy
bazel-bin/lcmtypes/drake-lcm-spy &
Also tangentially related would be https://github.com/RobotLocomotion/drake/issues/5857, though that is not on any near-term roadmap.