When you say "טבריה היא לא העיר שחשבנו" It means that the city of Tibries is not what you expected or thought about her.
This term is used a lot, for example- 'הוא לא מה שחשבתי' Means that you thought one thing about this person, but after you met him you suprised to find out that he is not what you were thinking about him.
That would be *היא לא העיר שחשבנו שהיא, or היא לא מה שחשבנו. The sentence given here is a confusing mix; this can just as easily be interpreted (or, rather, deciphered) as לא העיר שחשבנו עליה ‘not the city we had in mind’.
Tiberias has kind of a reputation for being chintzy and run-down, kinda like Blackpool or Atlantic City. Though last I saw it it was really cleaned up.