Right.
Hackney, as others have said, is east London. Haringey is a borough in the north of London. Harringay is a small area which lies at the centre of the geographical area pertaining to the London Borough of Haringey, which took its name when.
When you say you might be relocating to "Harringay/Hackney" I therefore you mean "Haringey/Hackney". However you did say you had just visited the place. So where exactly did you go?
I live in Harringay (obviously) and although it is somewhat down-at-heel I am not sure I would move anywhere else in London even if I could. The schools are great; there are superb transport links (we can be at Stansted or in Leicester Square in about 40 mins); there are three decent swimming pools a bus ride away, and canals and country parks can be reached by bike (and there are four excellent parks within walking distance of here).
If you want small, individual and arty shops, head to Crouch End or Muswell Hill. Ethnic food? Seven Sisters. Big shops? Wood Green has Mozzas, M&S, Primark, TK Maxx and more. Harringay Arena (on the north-east side of Finsbury Park) has sports, clothes and food shops etc.
Our street is most of the time very quiet even though we live five minutes from a major thoroughfare which never sleeps; buses are many and frequent and when you get off you will find decent greengrocers, a quality butchers and a plethora of Turkish restaurants which foodies regularly trek across the capital to visit.
As for south London, I don't want to start a Mumsnet "postcode war" but when I was a student I lived in the Oval and all I can say was the vibe was... interesting.
BTW I have also lived in Camden Town and Islington and I know the Holloway Road area well. If I could live anywhere in north London I would choose Islington because of the beautiful houses, good transport links and excellent shops and restaurants. Highgate is also lovely but way out of my league! Crouch End and Muswell Hill are more affordable but also achingly middle-class... although a lot of people seem to like that sort of thing.
If you need any more info, I'll be happy to help!
@HarringayBirder