Reliable, Free Flight Alert Website allowing multiple route combinations

Kayak.com allows you to create price alerts. So let's run through your criteria.

1. Free - it is, yes. Well, you have to sign up so you're giving them some information.

2. Sure, it's not just 'ex-NZ specials, but city specific, or multiple. For example, you can have a search:

   [Flights from SYD to CHC on a specific day, one-way)(https://www.kayak.com.au/flights/SYD-CHC/2015-03-27)

   or something more complex:

   Flights from SYD, or either Melbourne airport, to either Christchurch or Auckland, return, business class, on this specific date, but I'm flexible by +/-3 days on the return

3. Well it checks most that I care about. I know RyanAir in Europe isn't on it, but it covers most you'd want to fly with.

4. Weekly? You can choose daily or weekly (a tutorial on creating one has a screenshot of this if you want evidence

   Kayak's sample page showing what your alerts look like, aside from the emails

5. Well, as shown above you can specify return or one-way flights. And it doesn't even have to be to the same place - you can do a search from/to multiple airports, eg, I used to search BNE,SYD,MEL to YVR,PDX,SEA when I was looking for cheap flights last year from Australia to the Pacific North West.

Are you asking too much? Nope. It's a great tool and probably underused by most, myself included. This has reminded me I should set up more on it.