Disclaimer: Not a Kiwi but have played a fair bit over there, being Australian I have also ceased watching rugby
Looks like the Lions tour only hits the "major" cities in NZ and spends a lot of time in Auckland. It's a little like Sydney, in that you would expect more good courses. You have identified Titarangi which is the pick.
The first game is in Whangarei, north of Auckland. Avoid Gulf Harbour but the new/redone course Wainui looks interesting. If you wanted to venture up further north you obviously have Kauri Cliffs and Tara Iti assuming you can wrangle something. Heading north might also be your best chance for decent weather.
I did up trip up to Northland (info is 10 years old) and it was so windy we couldn't justify the fee at Kauri, but had a fun day at Waitangi GC and also enjoyed KeriKeri, albeit I wasn't overly GCA educated at the time. Paihia is a nice base up north.
Planning a trip to Christchurch later this year so will be interested if someone finds a diamond in the rough down there.