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विद्यालय splits as विद्या + आलय, so आ meets आ — two similar vowels joining into their long form, which is दीर्घ संधि. गुण संधि is the tempting alternative and it needs अ or आ to meet a DISSIMILAR vowel: नर + इन्द्र = नरेन्द्र. यण संधि turns इ, उ or ऋ into य्, व् or र् before a dissimilar vowel, as in अति + अधिक = अत्यधिक, and there is no such change here. वृद्धि संधि needs अ or आ to meet ए, ऐ, ओ or औ. The test in every one of these is to split the word first and then look at which two vowels actually met.