Cara,
The Radisson is very nice, though not as cosy as Jury's. My office is a couple of blocks along the street from the Radisson, and I never take the Z into the city. If at all possible I travel in by train. There is an NCP just round the corner in Oswald Street, but I would be wary of leaving my car there overnight. There is a better car park in Waterloo Street, just a bit further away, but I don't know how much they would charge for an overnight stay.
The Hilton has its own underground car park, which I believe is well looked after, but again I have no personal experience of it. The Marriott, nearby, has a decent amount of parking space at the back of the hotel, but it's not as nice a place to stay as the Radisson.
Maybe some of the other locals like Jay or Adam can make better suggestions.
Final thought - why not just hire a small car for the weekend and then you won't spend your evening worrying about the Z?
Best of luck,
Jim