Harry Potter and the Sorcerer's Stone was made during a big transition in the film industry—the move from shooting with film to shooting digitally. Columbus erred on the side of tradition and used film.
They also erred on the side of geographical accuracy. The Harry Potter books took place in England (well, in the Wizarding World parallel universe located in the U.K.) and nobody wanted to mess with the minds and hearts of Potter fans by shooting The Sorcerer's Stone in, say, Los Angeles.
Most of the shooting took place at Leavesden Studios in Southeastern England, with a few stops to locations throughout the rain-drenched whole of Great Britain.
Another fun fact: shooting took a long time, largely because of child labor laws. People frown on making kids work in general, but when it's necessary (unless you want Harry to be played by someone old enough to shave), it's governed by very strict laws. The kids could only shoot for about four and a half hours each day.
The rest of their time was taken up by normal kid stuff like school, which the producers established on the set to make sure that all the kids (and there were quite a lot of them if you include all the extras) got their book learnin' on. That let them make the movie without breaking the law, and without ruining the kids' lives in the process.