Cambridge most certainly is not posh. In the sense that Hyacinth Bucket isn't posh. But if you asked Hyacinth Bucket...
There are some pretty parts, but again these are frequently exaggerated, they're not that great, they're just the best bits in an otherwise not a particularly handsome place.
The Botanic Gardens... actually really small, nothing really to see or do, it's an ok place to eat a packed lunch.
The mathematical bridge. Is a non descript and again, very small bridge that you wouldn't even notice, and even if/when someone points it out, it's a bit "oh, ok, nice bridge?"
Parker's Piece, just a small bit of lawn between two very busy, full of traffic roads. In the summer it's dotted with shirtless sunbathers who for a reason I can't quite put my finger on, all look a bit soap dodger-esque and aforementioned students, posing, because again, everyone obviously must be so impressed by them in every sense.
There's The Cam (the river) which is romanticised with it's punts and gondolas. Truth is, you'll rarely see this anymore (it might be banned completely, or that may have been a rumour at the time) because so many people would go on them drunk that several fell in and drowned. It really honks in the summer months.
It's definitely multicultural. Very safe. Very diverse. Loads and loads of Chinese tourists for some reason, I never could work out what was the big draw to specifically Chinese people.
As a pp said, some of the surrounding areas are lovely. But it would still make Cambridge your default "big town".
Going on other posts, Brighton doesn't sound terrific for what you're looking for either, and like many others, I'd be looking at London if I were you.