So, if your first example was changed a bit (didn't use one), you could use both a or the, though they will have slightly different meanings.
A is not used before one because it's implied. 'A one' just becomes 'one'.
Let's change the first example to include the name of the bank you use (Frost Bank) Assume that this bank has many branches with the same name:
The bank I visit most often is 'the Frost Bank' that is located on the first floor of my office building.
In this case, you're emphasizing the location.
You could also say:
The bank I visit most often is "a Frost Bank" that is located on the first floor of my office building.
The first example would probably be used more commonly but the second example is emphasizing that the bank happens to be a Frost Bank (instead of some other brand) and the fact it's on the first floor of your office building is less important.
This becomes more evident when you try to split the statement into two sentences.
The first example doesn't split very well because where the bank is located is important to describing the bank.
The bank I visit most often is 'the Frost Bank'. It is located on the first floor of my office building.
This, if anything, implies that there's only one Frost Bank, which isn't the case... there are many of them (following the assumptions of the situation).
The bank I visit most often is 'a Frost Bank'. It is located on the first floor of my office building.
In this case, we haven't lost the fact that there are many different Frost Banks but the info we're conveying is what brand of bank you use.
Similarly, with your second example both 'the' and 'a' can be correct, just pay attention to what you're emphasizing:
My favorite club at the moment is 'a dance club' in Gangnam that I go to once a week.
Here you're emphasizing that it's a dance club (instead of a sports club).
My favorite club at the moment is 'the dance club' in Gangnam that I go to once a week.
Here you're emphasizing that the club is in Gangnam and that you go there every week. That it's a dance club is less important.