First Day in London Itinerary critique
 

Hi all! I'm leaving for London tomorrow (woohoo!) and will be there for two days before heading up to Northern England for school. This will be my first time ever outside of North America, and I'm going to be by myself for the first few hours that I'm there, so I'm a little nervous. Since I'm hoping to get to my hotel in Pimlico around 1pm, I'm going to have about 4 hours to explore before meeting up with a friend. I came up with a potential itinerary, and would love critique/suggestions. Since I've never been to Europe before, I don't know how jet lag is going to effect me, but I've heard that walking is a good way to stay awake. Here's my idea:

Take the tube from Victoria station to Westminster station
Walk around Westminster Abbey, Parliament, and perhaps walk across the bridge to get the view from the South Bank (I will probably follow Rick Steves' Westminster Walk)
Walk up Whitehall, and admire the buildings/Horse Parade/etc.
People watch in Trafalgar Square and then, depending on how tired I am, explore the National Gallery and Portrait Gallery - Out of these two, which one would you choose? Is it ok for the first day or should I stick to the outdoors and walking?
Walk down the Mall and into St James' Park
See Buckingham Palace
Take the tube back to my hotel

Is this too much for 4 hours? Any other tips? Thanks so much!

>>Take the tube from Victoria station to Westminster station<<

Where in Pimlico is your hotel? If in the eastern side (near Pimlico station or the Tate) you could walk up Millbank along the river to the Abbey/Parliament.

Your plan is fine -- I doubt you will want to spend much time indoors -- but if the weather is nasty either gallery would be a good respite.

The Portrait gallery is smaller and more 'accessible'/less overwhelming.

But the National Gallery is great and you could pick just one or two areas to explore . . .