To see all of those things in one late afternoon / evening is definitely pushing it. Big Ben is literally just over the river from Waterloo, so that won't be a problem. London Eye is right near Waterloo too, but the queues tend to be long, so not good if pushed for time. Last time I went on the eye, we went at 10pm and got straight on though, so if you really want to have a look, go later. Westminster Abbey, Buckingham Palace, Hyde Park and Trafalgar Sq are fairly near each other so could be done in a few hours. Tower of London is a bit out of the way and not much to see unless you go in (although Tower Bridge is nice).
Nicest way to travel is walking or bus, but easier to get lost!! Tube is easy and gets you to the door step of each place. Other modes of transport aren't applicable in central London.
Thanks alot this helps me greatly