You're going to have to walk a a bit whatever you do. You could walk all the way up Kingsway to Holborn tube and get the Piccadilly Line to Green Park, or down to Temple tube and take the District Line to St James's Park. In either case, you'llhave to walk across the Park to get to the Palace.

Your best bet is to cross the Strand, and get either the No9 from the bus along Piccadilly to Green Park tube station, or any bus going to Trafalgar Square and walk up the Mall.

http://www.tfl.gov.uk/tfl/gettingaround/maps/buses/pdf/aldwychquad-11500.pdf

The nearest Underground station to your hotel is Covent Garden on the Piccadilly line.

Nearest Tube Station to Buckingham Palace is Green Park, also on the Piccadilly line

I recommed to download the tube map , if you want to know some directions before you arrive in London (theer you will find the tube map everywhere).

The walk from your hotel to Covent Garden tube and from Green Park tube to the palace when you add the walk inside the two tube stations, equals about 2/3 the distance to just walk it. You are only saving a 200 or 300 hundred yards.

The walk is almost exactly a mile straight shot down the Strand and the Mall. Unless you are infirm (and if so the tube isn't that great an option) I'd just walk it. It is a nice stroll.

Janisj is right, it's a nice walk. There's no real need to take a bus or the tube. Lots of cafe and shops on the way if you want to pause somewhere.

I'm kind of partial to the walk up the Mall to Buckingham palace. Are you going for the Changing of the Guard?

oops -something happened there - should ahve said >>You are only saving at most 200 or 300 hundred yards.<<

Bit more than that down the Strand (if you're comparing walking with buses).