What's the correct spelling of the Danish city: Ålborg or Aalborg? Thanks!?

Answer 1

Yes, both are the same. But it is not to make it more "phonetic". The letter å is not part of English alphabet (as ø and æ). So, to make it easy to be typed, these letters chage (å changes to aa, ø to oe and æ to ae).

Answer 2

Both. The double a in Danish was swapped to å in all words to make the language more phonetic, but place names kept the double a. It makes no difference which one you use - it's pronounced the same and Danes recognise both.