I'd say the sense of くらい is "to the point where", "so much so that", "to the extent that".
学校の敷地が狭い, "school grounds are small", modifies 都会, "[big] city", giving "In big cities, where school grounds are small".
中庭のないところもある means "there are some places that have no courtyard"
Put them together and add くらい and you get "In big cities, where school grounds are small, to the point where some places have no courtyards"
Add だったので、感動もひとしおだ 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".