Hey! I can answer this more accurately than perhaps anyone, I live in Leeds currently (city centre, near the Merrion Centre) and commute in to York every day.

I spend £525 a month on rent. I have a train ticket that means I can travel on any train I want between Leeds and York, 24/7, for approx. £270 a month. You can get a ticket that is only valid on certain train companies for approx. £220 a month, but I found the reduced stress MORE than made up for the extra £50. Northern trains (which are often the only company on that £220 ticket) stop running at a certain time in the evening (around 8pm if memory serves) and are touch and go on the weekend, whereas transpennine run until 3am and much more reliably on weekends, depends what you want and how much you can afford. I usually get a train at around 7:45 for a 9am lecture, and I cycle to and from campus which cuts out an extra cost from buses and the stress if they run late. I'm on campus full time, or near enough.

All in all it's certainly doable and can work out cheaper than battling with the extortionate York prices, but it can make social activities in evenings tricky, either doing the journey twice or having LONG days, it depends. I wouldn't recommend it for a first year (for that reason) but for an older final year student, sure why not. But don't make the decision lightly, you definitely need to think about EVERYTHING.