I prefer #1, but #2 is just as good if you omit some words. #1 has two interpretations: a) We went there (Rome, for example), but our purpose for going there was not to visit the Sistine Chapel. b) We didn't visit the Sistine Chapel. #2 is the same as: We didn't visit the Sistine Chapel. We didn't go to the Sistine Chapel. We didn't go visit Sistine Chapel.

These both sound fine to me.

By itself, the first is ambiguous. (It could mean ‘We went (somewhere) but our reason for going wasn’t to visit the Sistine Chapel.) The second is a little odd. What do you mean by ‘go and visit’? In the positive you can add an unnecessary ‘go’ but it doesn’t sound natural in the negative.

Both are correct. #1 is maybe a little more common, but I use both forms in my daily life. Good luck!

“We didn’t visit the Sistine Chapel” sounds smoothest to me.