An alphabet is a standardized set of signs to display parts of a spoken language - it may be pictographic and display a whole picture as a symbol for a specific thing, it may be phonographic and display one sign for a syllable or ideally just one sign for a single phoneme. (A phoneme is the smallest posited structural unit that distinguishes meaning in a language.)
One language in which one phoneme is represented by one sign is the georgian Alphabet, which therefore would be an ideal choice for the University of Babel.
Letters
ა /ɑ/
ბ /b/
გ /ɡ/
დ /d/
ე /ɛ/
ვ /v/
ზ /z/
თ /tʰ/
ი /i/
კ /kʼ/
ლ /l/
მ /m/
ნ /n/
ო /ɔ/
პ /pʼ/
ჟ /ʒ/
რ /r/
ს /s/
ტ /tʼ/
უ /u/
ფ /pʰ/
ქ /kʰ/
ღ /ɣ/
ყ /qʼ/
შ /ʃ/
ჩ /tʃ/
ც /ts/
ძ /dz/
წ /tsʼ/
ჭ /tʃʼ/
ხ /x/
ჯ /dʒ/
ჰ /h/
This would be an example for a written text in the georgian alphabet: 