use of くらい in this sentence Speaker is in a conversation about the courtyard in his new school that he just transferred to (from tokyo). > Because, in the (old) school site, as tokyo is very cramped, there was no courtyard (?) , I'm especially excited (about this school's courtyard).

I'd say the sense of is "to the point where", "so much so that", "to the extent that".

, "school grounds are small", modifies , "[big] city", giving "In big cities, where school grounds are small".

means "there are some places that have no courtyard"

Put them together and add and you get "In big cities, where school grounds are small, to the point where some places have no courtyards"

Add and you get "Since it was the case that in big cities, where school grounds are small, to the extent that there are some places that have no courtyard [at all], I was delighted"

More idiomatically: "In big cities school grounds are so cramped that some schools have no courtyard at all, so I was delighted".