Hello! I used to work in the wine trade and hold the WSET Diploma - tastings were my bread and butter!
If you like an NZ Sauv, that would suggest that you like a drier, fresher flavour, so I would suggest avoiding New World reds, which are often very big and meaty, and looking at younger, fresher reds from the Old World.
French Pinot Noirs can be both expensive and a bit hit or miss unless you're spending big bucks, but there is some interesting stuff coming out of Romania and, rather weirdly, Wales.
You may also enjoy Portuguese reds such as Duouro, which are pleasing but without the big tannic hit of many French or Spanish reds.
German red wines aren't well known in the UK (and have a bit of a reputation for being 'thin' when you can get them), but some good stuff - mostly Pinot Noir - comes out every now and again.
The absolute best for a red wine novice is Italy - Chianti is light and refreshing and always goes well with food, while a Valpollicello or Nero d'Avolo will be a little fruitier and drink well alone.
I am a huge fan of Lidl and Aldi's continental wine lists, which are really well selected and a good price, and a good opportunity to try stuff out.
Good luck and enjoy!