"Isn't that the place WHICH kids under 12 can't enter?" - Is it correct to use 'that/which' when it refers to a place?

The word where replaces locative phrases. These are the types of phrases usually represented by locative preposition phrases:

• That's the restaurant where I met my wife.

In the sentence above there is a phrase that it missing from the relative clause:

• That's the restaurant where [I met my wife ____ ]

That gap tells us how to slot the information represented by where into the clause. We can mentally reconstruct the clause like this:

• That's the restaurant where [ I met my wife in that restaurant ]

Here the word where is indexed with the missing locative phrase:

• That's the restaurant where_(i) [ I met my wife _______(i) ]

Where versus which/that

Very often we have a choice about whether to replace the whole locative phrase or just a noun phrase within it. When we replace the whole locative phrase, we use the word where, if we just replace a noun phrase within the locative phrase we use which or that:

• That's the restaurant where I proposed to my wife [ in that restaurant ].
• That's the restaurant that I proposed to my wife in [ that restaurant ].
• That's the restaurant which I proposed to my wife in [ that restaurant ].

If we use where to represent a noun phrase or which/that to represent a locative (preposition) phrase the results are ungrammatical:

• *That's the restaurant where I proposed to my wife in. (ungrammatical)
• *That's the restaurant that I proposed to my wife. (ungrammatical or different meaning)
• *That's the restaurant which I proposed to my wife. (ungrammatical or different meaning)

The Original Poster's examples

1. The Queen Alice is the theatre that I go to the most.

2. Isn't that the cinema which kids under 12 can't enter.

Now the original sentences both have relative clauses using the noun phrase the place as an antecedent. Relative clause with place in the antecedent exhibit exceptional behaviour. To simplify the situation and make things a bit clearer I've changed the nouns. At the end I'll explain why. But this next section should clarify the situation about the word where.

In sentence (1) there is a gap in the relative clause, but the gap represents a noun phrase inside a locative preposition phrase:

• The Queen Alice is the theatre that I go to _____ the most.

The antecedent for the relative clause is the noun phrase the theatre. We interpret the gap in the relative clause as referring to the theatre within the clause:

• The Queen Alice is the theatre that [I go to that theatre the most].

Notice that in the sentence above, we still see the preposition to. This preposition is the head of the locative preposition phrase. Because the locative phrase isn't being replaced, we use which/that and not where.

In sentence (2) the gap in the relative clause doesn't represent a locative preposition phrase but a noun phrase. It represents a Direct Object, not a Locative Adjunct or Locative Complement. It therefore uses which:

• Isn't that the cinema which [kids under 12 can't enter [that cinema]].

We could use where here. The meaning is ever so slightly different:

• Isn't that the cinema where [kids under 12 can't enter].

This relative clause means something like:

• In that cinema kids can't enter

  ... as opposed to:

• Kids can't enter that cinema.

Relative clauses after place

Defining relative clauses after the word place are unusual. Most importantly, we can omit the word where from such relative clauses. We can't do this if the antecedent is a different noun:

• That's the place we ate last time
• Dublin is the place I want to live.
• That's the place we saw that incredible film.
• This is the place they kept the prisoner.

We can compare those to:

• *That's the restaurant we ate last time. (ungrammatical)
• *Dublin is the city I want to live. (ungrammatical)
• *That's the theatre we saw that incredible film. (ungrammatical)
• *This is the dungeon they kept the prisoner. (ungrammatical)