The phrase "I should visit" is correct and can be used in written English.
Example: "I have always wanted to see the Eiffel Tower, so I should visit Paris one day."
I should visit the main street before I left, she said.
I went back and forth over whether I should visit him in his last months.
I asked Ms. Ptak where else I should visit, and she pointed across the street to the Spurstowe Arms.
Thanks to all for your suggestions for where I should visit for the magazine's Food & Drink issue.
The prime minister was determined I should visit a police station at which all the officers were women.
Perhaps I should visit that lovely tool shop in the precinct to look for a torque screwdriver.
I knew Ken had no interest in music but I suggested we should visit him and ask what to do with the Teardrop Explodes.
But then, I don't want to simply offer you a list of places I think you should visit.
As Borat would say: "That is quite a good deal and I think you should visit the site and purchase those items".
"It's a place that I think people should visit.
"Whenever people ask me if they should visit Greece I tell them to go to Turkey instead".
