Take your choice, (If you don't have too much luggage), take the tube. That is the least expensive way, and probably the quickest. Take the Yellow or Green Line to Westminster, and walk across The Westminster Bridge. Here's a view Of Marriott County Hall from The Westminster Station.
That's Marriott County Hall, with The London Eye, to the left!
Walk thru this entrance to a very special place!
I would take the tube. As jerry said it depends on how much luggage you have.
you can either go circle / district line as suggested.
or you can take bakerloo line to Baker Street then jubilee line to Westminster for short walk across bridge.
good link for tfl which allows you to include options if you have mobility issues or don't want to use stairs:
You are the man!
That is the way to go!
ams10, once you get out at Waterloo, head toward The London Eye. You will see The Marriott next to it on the left!
You will know you are going toward County Hall when you see The Eye coming from Waterloo Station. I had just had a Burger King at Waterloo and was walking back to C-H from there. That is The County Hall building to the left and in front of the Eye. You have to go to the other end of the building to get into the Marriott.