Oh, it is really nice there, Iain, take her to Deutsches Museum
, don't miss it as long as you hang out in München!!! It is a kind of technical museum... about inventions... from the history of aviation, to the history of sailing... and lots of other things.
Imagine a huge ship in the middle of a hall... and huge helicopters upstairs... and airplanes... and there is section for environment, energy, fuel cells, for engines... it is very interesting and entertaining, in the same time.
It is that kind of museum where one would take one's kids, when they are between 11 and 16... but of course I saw with when I was 23 and still enjoyed it a lot.
My parents also enjoyed... okay, both are engineers, so no wonder...
Well, it is not a specificly "romantic" place to go... but you will surely not regret.
If you want romantic, take her to the Pinakothek der Alte - to look at paintings (if she likes that stuff, of course). It is free on Sundays. Have fun!
You need about 3-4 hours for Deutsches Museum... and as Showem says, it is not cheap... no, neither on Sundays. But it is worth the money, I would say.