I am currently a freshman attending GWU and participating in the GWU NROTC Unit, although I don't attend Georgetown I can provide insight on how often we meet and can pass along somethings that I have heard about being a crosstown student from my peers. In regards to having to commute to GWU there is a mandatory NROTC class twice a week that lasts 1 hour(days/times depend on the class and grade level), these are usually Monday/Wednesday or Tuesday/ Friday. Also there is a mandatory Leadership Lab on Friday mornings from 7-9:15 (however everyone must be present by 6:30). In addition to classes there are also mandatory PT sessions (2-3 per week) there are some offered on the Georgetown campus but one of the sessions must be completed on the GWU campus/National Mall. Now about actually getting to GWU, Georgetown is not near a metro stop but Georgetown does provide a free shuttle to the closest metro stop (across a bridge and in Virginia, roughly 15-20 minute walk). Currently majority of the Georgetown students will split the cost of an uber to GW (pretty cheap) or some will even bike over. All of the Georgetown students that I talk to say that they don't mind the commute and they all seem to be very close with each other.
Lastly, in regards to the program itself, this unit is consistently ranked among the best in the nation and with the location of our unit being in DC we are privileged to have very important guest speakers come in and talk with us (ex. MCPON, Sgt Maj USMC, and many admirals/generals). Also we have access to many high level/interesting events and often have the same off campus events that USNA Mids attend. Its a great program and location and if you're son wants to reapply to USNA our unit has a great track record with re-applicants.
Hope this helps, if you have any other questions please feel free to message me.