'Runaround' bike

I currently share a car with my wife so it makes no sense financially for me to have my own car (unfortunately for me!)

Can anyone recommend a cheap runaround bike for around 1k? I was thinking of a Hornet/FZ6 or something although I've not looked at the bike market for a while. I don't need to commute on it so it will just be used for local running around now and then.

The Monster will stay as my fun bike, I just don't fancy leaving it around London or subjecting it to short trips etc