London - need guidance with stay and train

London has no centre, or you might say it has two (historically it was two different cities) which have merged into one.
There is no one central "good" place to stay. But anywhere within the "Circle line" will have good transport to everywhere.
For an absolute beginner's guide to getting around London, and some maps, see this leaflet here: http://content.tfl.gov.uk/london-visitor-guide.pdf
This is produced by "Transport for London" (TfL) which runs all the buses and trains.

Getting from Heathrow to anywhere in central London: There are two options, "fast and expensive" = Heathrow Express non stop train to Paddington. "Slow but cheap" = Piccadilly line (underground). Which is better depends on budget, time, and where exactly you are staying.

That should get you started.

Get to the Tower of London as soon as it opens, before the crowds. Buy the tickets online now. This way you will not have to wait in line at the attraction wasting precious time. There is a changing of the guard at the Tower. I have read from other posters that the Changing of the Guard at Buckingham Palace is not all that its cracked up to be. I enjoyed the Tower version. It was smaller, you could see it up close, and didn't take as long.
For my upcoming trip to London, I logged onto Google Earth and placed thumbtacks on all the different places that I wanted to see. This helped me to visualize the most efficient order of things to see.

If you stay on the Paddington Station area you can save time on transport and get to your hotel at a reasonable hour in the evening. There are several Tube lines running from that area. Plot out your day to see what you want. Changing of the guard at Buckingham Palace is around 11 am, but not every day. It may be difficult to fit that on with the other things. Each site and experience will take a couple of hours or more. You might visit the Tower when it opens on the morning, spend a couple (or a few) hours there. Then you could go to the London Eye; half an hour for the experience but it may take a while to buy tickets and wait in line. Head to Trafalgar Square for lunch and looking around; restaurants, museums, theaters are there.

You do not have time in one day to do all that. The Tower of London and London Eye are ticketed attractions, and you can spend a lot of time standing in line if you do not purchase in advance to skip the line. I suggest you plan on one in the morning, and one in the afternoon, and book in advance.

The "changing of the guard" at Buckingham Palace is highly over-rated. Maybe I am cynical as I am small (5'2") and can never see a thing. We much prefer the guard change at the Horse Guards if you are interested in pageantry and the like.

Trafalgar Square is a place to walk through on your way to somewhere else. Lots of history represented there, but you need to know in advance what you want to see and appreciate there. The crowds can be huge.

You can catch bus #15 from there to the Tower of London if you like. Slow, but it beats the Tube in terms of comfort, in my mind.

you can stay anywhere and get anywhere, but whats your budget thats the most important factor

Are u talking this upcoming Monday? How late will you be arriving in the evening? What's your budget for a hotel room?

Few things::

1. It is Trafalgar Square. No apostrophe. Its nice ( Lion statues, National Gallery and Nelson's column ) but why there as opposed to the iconic Parliament Square ie. Houses of Parliament, Big Ben and Westminster Abbey? BTW you can walk from one to the other in 15 minutes. Or take the tube.
2. The changing of the guard is overrated. Unless you get good first row look see you won't see much. Horse Guards more interesting. However if you want to see the Tower Of London ( and I believe you should )go there first thing Tuesday morning and be in the first group of people entering. Head right to the Crown Jewels then enjoy the rest of the Towers intriguing history. Hours can be found on their website or I believe in TimeOut London online.
3. If its a clear evening the night you arrive and the Eye is still operating might consider seeing London at night by riding it.
4. Its the London Underground that you'll be riding and there are stations throughout London. Fairly easy to get from one part of the city to the other by riding it. If you share your hotel budget it will easier for us to suggest a neighborhood to stay in.
5. Last use the GOOGLE maps satellite image. Type in Big Ben London in the search box. You'll be able to see how close and far sites are.

GREAT city. Enjoy.

Book the London Eye in advance - queues can be very long. It should still be possible to get advance tickets even if you are talking about this coming Tuesday.

Claudia - thanks for the info!
It will be the 3rd week of June so we still have some time to get things together. We will be arriving at the hotel @6:30pm. As far as budget, we are flexible because it is a short time, however, we do not plan to be in the hotel a whole lot $150-$300 at the top end.

Thanks everyone for the info and suggestions! I will buy tickets online for the London Eye and Tower. I am still looking for a place to stay.

You have made your decision for the sights you want to see and they are good choices. I simply want to add my two cents regarding the changing of the guard at Buckingham. My research prior to my trip last fall indicated that the ceremony was, indeed, a bit ho-hom and missable. However, we changed our minds in the morning and decided to see the spectacle after all. It was a spectacle that we truly enjoyed. We got there early enough that my 5'2" self and husband secured a decent spot on the steps of the monument. For me, I liken the guard changing to that of a football game. Observing the attendees and the pomp and ceremony leading up to the changing of the guard is the real show. The selfie sticks held up in air, people who are shoo'ed off the lion ramparts by the guards, people on their toes craning their necks and juggling for position - this is the real show...and it was an experience I'm so glad I had.

Your're welcome but I wouldn't pre book the Eye. Weather and your stamina could cause you to miss your appointed time. Just saying.

No promises any rooms are available at these places but worth research for your dates.

The Amsterdam in the Earls Court neighborhood. The Vancouver Studio Apartments in the Bayswater neighborhood or the Pullman by St. Pancras. The latter is a large business hotel. Might also check the much smaller Alahambra Hotel in the same area. Check TripAdvisor reviews for all of them to help narrow the options.

Good Luck

I have to agree with the others that the Changing of the Guard was a disappointment and took a LOT of time (2+ hours with waiting). That's time you do not have to spare with one precious day!

The evening you arrive, if the weather is good, hightail it to the London Eye for an evening ride. Have a pub supper near your hotel.

9:00 Tower of London (see crown jewels first, then 10:00 Beefeater tour and White Tower (we found the Tower took 3 hours easily but by arriving at 9:00 we were in advance of the late sleepers!)

13:00 As Rick Steves suggests, grab a picnic (There's a Paul right across from the Tower), catch a boat at Tower Pier, and relax with lunch on the Thames while cruising to Westminster Pier. (Weather permitting)

14:30 Walk from Westminster Pier to see Westminster Abbey (You have time to tour Westminster Abbey if you like), Parliament buildings, and Big Ben, then up White Hall past Horse Guards to Trafalgar Square. (Rick Steves book ahs a nice walk outlined in this area that is very informative) Stop in St. Martin's in the Field for a coffee/tea break in the Cafe in the Crypt.

Late afternoon/evening, hit the London Eye if you did not the night before or add on some other sight you might have in mind.

I would stay as centrally as possible. Covent Garden/Soho is right in the middle of the action, so to speak.

Forget Changing of the Guard at Buckingham Palace as it won't fit in with your plan. Go to Horse Guards for the Four O’Clock Parade.

0900 Tower of London
1200 Tower Bridge (photos)
1300 St Pauls Cathedral
1500 Trafalgar Square
1600 Horse Guards (Four O’Clock Parade)
1700 Houses of Parliament & Big Ben (photos)
1800 London Eye

There is a café inside of the Tower of London. You can eat there, or take out something and eat while you are walking around looking at the outdoor parts. There is also usually an ice cream stand.

Thank you all for the wonderful and helpful suggestions. We have decided to to stay closer to Trafalgar Square.

As suggested, I have purchased online tickets for the Tower of London and the London Eye. The London Eye - I purchased the anytime tickets - a little more $ but that way we can do it Monday night (if okay weather) or anytime Tuesday. We plan on getting to the Tower of London by 9am. My DD is very excited to see the crown jewels! The ideas about where to eat are great and depending on the weather may just get the picnic lunch. We are planning on see the Horse Parade at 4pm and Westminster Abbey. Thank you for the time tables. It was a great help!! Totally excited!!!!!

After seeing the Tower walk up to the glass covered Leadenhall Market. 10 minute stroll at best. It's lovely. You could have lunch there and if DD is a Harry Potter fan have her look for the entrance to the Leaky Cauldron.

If you are even more adventurous you could take the tube from Tower Hill take the district/circle line (green) one stop to Aldgate East. Take a 15 minute walk to the always interesting Brick Lane. http://www.visitbricklane.org

The # 15 red double decker bus will get you from the Tower to St Pauls to Charing Cros/Trafalgar Sq.
Sit up top for a great view coming down Fleet St and The Strand.
https://tfl.gov.uk/bus/route/15/

We had a great lunch at Wagamama after touring the Tower of London, it is super close by and is fast and well priced. It is located in the big glass building next to the tower.