Yes that’s a good, easy way to do it. Metronorth, to 125th street station, and taxi to the medical school.
You can take a yellow or GREEN taxi from the Harlem/125th street station (green ones run north of 110th street). 125th street can be really packed depending on the time of day. You may want to ask that the taxi take you on 126th street, if 125th is really packed.
If you want help navigating inside of NYC, think about downloading the citymapper app. It’s pretty good for telling you how to get from Point A to Point B and also tells you when there’s a problem with the subway line.
Public transportation for that route would prob. be a city bus headed west to St. Nicholas Avenue and then transferring to the A train uptown. You can also walk from the 125th street station to the A train stop, about a 15 - 20 minute walk. To take a bus or subway, you purchase a Metrocard in the Subway stations, so you can get one across the street from the 125th street train station inside of the 4,5,6 greenline subway station, using your credit card in the metrocard vending machines. Then come out and take a bus headed west across town. Take the M100, or the M60. To get the M60, you buy a paper ticket on the street using your Metrocard and hop on any of the open doors (supposedly makes boarding this bus faster and makes this bus a faster, express bus).
The citymapper app will tell you when the buses are due at which stops.
I am not a big user of apps, but one of my favorite is the onTime app that provides Metro North train schedule info. The app also tells you which platform your train will be departing from, and if the train is running late.
Returning from the medical center to 125th, it will probably be easier to hail a taxi than look for your Uber. Best of luck.