Hello there,
I am a non-native English teacher in Kyoto, Japan.
I would like to know the usage of "would".
Please take a look at these 2 sentences below.

a: I would like you to visit Todaiji Temple first.
b: I would want you to visit Todaiji Temple first.

Is (b) correct? Doesn't it sound weird?
If it is a normal and grammatically correct one, do the two sentences have the same meaning?

I think this question looks strange to you, but I really want to know your opinions.
Thank you for taking time.