1st day in London

Venture across Westminster Bridge which is outside your hotel door and walk straight up to Buckingham Palace which is only a short distance. It doesn't get any better than this!!

I agree, the area your hotel is in is right near many top attractions -- Houses of Parliament, London Eye, Westminster Abbey, and a short walk to Trafalgar Sq. & Buckingham Palace is a bit further out. If you don't feel like walking too much, you can get the hop on hop off bus on Westminster bridge and tour the city that way.

Definitely walk across the bridge! Visit Westminster Cathederal, walk through Whitehall, and if you're into "modern" history, you can visit the Cabinet War Rooms (under Whitehall) which is the big command bunker from WW2. When visiting the Tower of London, I'd also take a walk across the tower bridge. I found it worthwhile to pay the fee and take the elevator to the upper level foot bridges. A great view of the city. If you get over to Blackfriars Station (you can take the Tube), it's a short walk to the middle and inner temple (where the barristers have their chambers). In there you can visit the Temple Church (email their rector to check the current hours). The Temple Church is an orginal Knights Templar site, and if you saw the DaVinci Code you'll recognize the interior. Also from Blackfriars, it's a nice walk across the Millenium Bridge to the Tate Modern, as well as the Globe Theatre. One of the nice things about walking around London is how if you just go two or three blocks off a "main drag", you can find little villages within the city. You'll see blocks of flats, perhaps a tiny park, as well as a block or two of shops and the local pub. While "touristy", I'd suggest taking a ride on the London Eye after dark. It's a nice way to finish off the day and it's a beautiful view of the city after dark. Another nice walk is from the Picadilly Circus area down towards Covent Gardens (aka "Theatre Lands"). Just like New ork, you can get good deals on same-day tickets from the "TKTS" booth (as well as private brokers) in Leister Square.

I'd come out of your hotel and start with a walk along the South Bank heading in the direction of Tower Bridge. This is probably my favorite walk in London. This website has some good walking guides that you can download for the South Bank area:
http://www.southbankwalks.com/TheGuides.html

Walk along the thames (south bank) or Embankment (north bank); or Westminster Abbey, Big Ben, Parliament, Whithall to Horse guards, Trafalgar square. From there you can do National gallery or fleet street (east), or Piccadilly (west) to Green park or Hyde park. I tend not to do any Tube travel on my first day. just like to walk among the familiar suuroundings in the west End (high tourist value area). If you are arriving at Heathrow at 9.30, you will probably get to your hotel close to noon, so you really only have afternoon nd evening Another option, if you are not familair with London, is the Hop-On, Hop-Off bus to get a good orientation that first day

I'd recommend a relatively unplanned day without any time-consuming commitments so you can scamper back to the hotel in afternoon when the jet lag kicks in. If you leave your hotel, turn right, and walk along the Thames, you can spend more than a few hours idling along the South Bank. You could take a ride in the London Eye. (It will be right there, practically looming over your hotel.) Westminster Bridge is itself an attraction, so take your time walking across. Parliament, Big Ben, and Westminster Abbey are at the other end. Seeing the Abbey is well worth it, but takes some time, so you may want to save that for later. You can walk up through Whitehall -- the home of the UK government -- to Trafalgar Square, location of a couple of the best art museums on he planet. (Hint: Many of the larger museums in London have decent and surprisingly good cafes, including the National Gallery at Trafalgar. That can save a lot of time versus blundering around blindly look for a place to eat.)