Can I say
go to the centre?
Or there is difference in the meaning between
into the centre
to the centre
Can I say
go to the centre?
Or there is difference in the meaning between
into the centre
to the centre
That depends on context. Namely, whether the "center" (or "centre") under discussion has an interior.
If there was a large circle drawn on the ground with people standind around it -- perhaps some sort of ball game? -- we might say "Now, John, go to the center". We would not say "in to the center" because there is no "in", it's all outside.
If by "the center" you mean "the Euler Mathematics Study Center", and this is a building, and we are standing outside of it, you might say, "I am going to go in to the center". But if we were miles away and you were talking about driving to it, you'd probably say, "I am going to drive to the center", not "in to the center", because at that point we're not really thinking about inside versus ouside but more about this part of town versus that part of town.
We often talk about being "in such-and-such city". So you might say, "I'm going in to the center of Boston". But frankly I think fluent speakers would be more like to just say "to". But any example where we talk about being "in" a place, you could probably say "in the center" or "in to the center" of that place. (I can't think of exceptions but I don't want to rule them out.)
Using into
suggests that there is some kind of building or structure or enclosure to enter. You could argue though that the centre is it's own structure of some sort (like a force field) and there is a border between the outside of the centre and the inside.
Let's go into the centre
It basically means that we are going inside
the centre.
Now there is no structure or enclosure or bordered off area to enter.
Let's go to the centre.
We wouldn't be entering any place or exiting any place. We are simply going towards
the centre and once we've reached it, we will have gone to the centre.