Perhaps I'll just clarify my point....
As an ATCO who is involved in NATS' recruitment, both at assessment days and interviews, I would recommend you make as many visits as possible.
As rodan says, if you are applying to NATS then I wouldn't be too bothered if you visited non-NATS units, although I think it's beneficial to see both en-route centres (ie. NATS in the UK) and airfields.