Hi,
I don't live there but I did visit (I'm applying to Durham in a couple months for undergrad psych) and I'd say it seemed relatively skateboard friendly. The only real problem was how hilly the area is- If you're going to one of the sites up the hill, you will not be able to get there by skateboard. Seriously, I had to go the long way round (through grass and things) because I couldn't even WALK up the hill, I just kept tumbling backwards. (Then again, I do have mobility issues, but I know I wouldn't have been able to bike that either).
However, the town itself seems to have relatively good roads and pavements, so I think although getting to class may prove challenging if the science site is at the top of the hill, you'll probably find that the rest of the town (the shops, library, etc) are eay to get around by skateboard.
Good luck!