Staying at the Premier Inn County Hall.
It appears Waterloo station is slightly closer, but would it be easier to walk across the bridge to Westminister station?

For most of the places you could be coming from Westminster is a more convenient station to use

If, for example, you are coming from Heathrow then taking the Tube to Hammersmith, walking the few feet to the adjacent platform then taking the Tube to Westminster, leaving by the Bridge Street exit and crossing Westminster Bridge is easier than taking the Tube to Green Park, walking though tunnels to the Jubilee Line, then Tube to Waterloo

Waterloo is really, really close to Premier Inn (I stayed there last year, and it was actually really great). I found the Waterloo tube station very convenient and when I got sick of the tube, I caught the pale green line bus, which is THE bus to take if you want to get around the South Bank and get the view. But yeah, Westminster is very close as well, though I never used the station there...

Play it by ear according to where you want to get to. For some trips, Waterloo may be more convenient, or Westminster, or a bus. Don't forget too that you can also walk across the Hungerford Bridges to Charing Cross - or you can walk along the South Bank all the way to City Hall and Tower Bridge.

Buses from there:
http://www.tfl.gov.uk/tfl/gettingaro...loodr-2289.pdf

Or you can get boat trips from Waterloo, Embankment or Westminster piers, I should have added.

"<i>Waterloo is really, really close to Premier Inn (I stayed there last year, and it was actually really great). I found the Waterloo tube station very convenient</i>"

Waterloo is close . . . but it only makes sense for <i>some</i> journeys/situations. You need the big picture - where are you going, where are you coming from. The closest tube station isn't necessarily the 'best' tube station for a particularly trip.