何処のツタヤに行くの？って英語でなんて言うの？

The first sentence is the usual spoken form in the UK.. The second sentence seems more formal, even a little antiquated, although it is useful if you wish to stress 'which' a little more strongly.
EX
A: Which Tsutaya store are you going to?
B: I'm going at 10 am this morning.
A: No, I said to WHICH Tsutaya store are you going?

Which' is the expression for asking information on a particular thing if it has options, in this case 'which' store will they visit as there are many stores.
To 'visit' a place/location is the term used to go somewhere, ex. "I went and visited my friends in town on the weekend".
The term 'store' is the same as a shop.

When I ask this question, I want to know: which of the many TSUTAYA stores in the region are you going to?

Example one is asking for a point of reference, like, "The park near the train station." This question will help you create an open dialog about stores in your region while also finding out witch store they are going to.
Example two is just adding more to the question, "Which TSUTAYA are you going to?". It is creating conversation about the amount of TSUTAYA stores in your region while also asking the question.

Many different ways to ask this. Simply using wh question or asking for a location.All the way to stating where you use and allowing other person to respond that way

When you want to ask a person which TSUTAYA store a person is going to in the region, then you may ask in the following ways:
-Which TSUTAYA store are you going to?