I would use the following: Which/What places would you like to visit? Which/What places would you like to go to? Which place would you like to go to first? What would be the place that you'd want to go to first? What is the purpose of your visit here? (very formal. 'Why are you visiting here?' is an informal option). Usually we use "which" when there is a choice between a limited number of options, eg Which place would you like to go to first, Beijing or Shanghai?

Which assumes a specific range of options. It could be followed up with "of those" or "out of those choices." Examples: -Which, of those places, would you like to visit? -Which, out of these options, is your favorite? -Which is your favorite food - pizza or hamburgers? What is more general and broad, not specific choices. Examples: -What is your favorite food? -What is your name? Corrections: What places would you like to go **to** / visit? Which place would you like to go **to** first? **What places would you like to go to first?** For what purpose **are** you visiting here?

you use the wich when you have many choices

you use the wich when you have many choices

"Which places would you like to go *to*" "What place would you like to go *to*" "Which place would you like to go *to* first" In these sentences, "to" can only be used with "go" and not with "visit" "For what purpose you're visiting here?" is an incorrect sentence. The correct way to say this is "For what purpose *are you* visiting here?" But this still sounds unnatural. A more natural way to say this is "Why are you visiting here?" Hope this helps!