Now to see how these families all come together -- so much fun, so little time!
You will love York -- it is the most amazing place! If you are taking the train from London to York, you'll come in fairly close to the convent. With luggage, however, I would encourage you to take the bus rather than walk; its just easier.
Now about what to see in the city while there; since you've not been to York, that's pretty easy. As I mentioned, at the convent, be sure to visit the museum to learn about the women who ran and taught at the school. Then, take a walk on the city walls not only to get a terrific view of the city, but see some of what the students would have seen -- the skyline is little changed except for the few modern structures on the edges. From the convent, walk into the city centre through Micklegate (one of the original city gates) -- it was the most direct way into town from the convent. The city centre is pedestrian-friendly these days, so its easy to wander around and take pictures. Find the York Assembly rooms; it was the place for balls and concerts, and students often attended them. The small shops all along the streets from the convent and in the city centre are virtually unchanged (except for the obviously late 19th c and more modern ones), and student account books indicate that the students did their personal shopping here (though we don't have names or addresses). Clifford's Tower is another landmark that the girls would see, as is the York Museum (now a museum it was a prison at the time the Goodman girls were in York).
So, there you go; if you can do all of that in two days I'll be impressed. You'll have a good feel for how the girls felt when they first arrived in the city, and it will bring a new dimension to you family history.
Have a great time!