On day in London: What to see and where to stay

take the train from Gatwick to Blackfriars station and stay here

http://www.premierinn.com/gb/en/hotels/england/greater-london/london/london-blackfriars-fleet-street.html

only you know what you want to see....

Some of the best museums in the entire world are in London, but you might only have the time or energy to see one or two of them in a day. Are you an art fan? History? Modern (or antique) design?

. . . or interested in doing the tourist "must-do" things?

If you stay where the first poster suggested, I'd suggest following Rick's City of London walk (you can find it in his London book or on his app) in the morning. The walk includes St. Paul's, so you could opt to spend a bit more time in there as well. Then at the end of the walk, head to Borough Market for lunch. After that, let your interests dictate your afternoon, and pick the museum that interests you most. Use the Tube to get to wherever you choose. Some options: Interested in art? Head to the National Gallery. Ancient history? The British Museum. Tudor history? Hampton Court Palace (train from Waterloo; this will definitely be a packed day, but I think Hampton Court is really interesting). WWII? Churchill War Rooms. After any of the museums, duck into a pub for a pint. Then maybe to the West End for a show. It's a busy day, but a good balance of activities, I think.

Of course, there are many other potential day-long itineraries. What are your interests? Have you been to London before and what did you do then?

Start at Parliament Square.

Thank you for your reccomendations, Blackfriars looks like a good starting point.

I am huge fan of London Walks, no need to book in advance, just show up and pay 10 GBP to the tour guide.
www.walks.com

The National Gallery is one of the finest art museums in the world, it collects only European painting from the late medieval era to about the 20th century. It is free, with a donation appreciated.

If you stay in the Premier Inn that ramblin' on suggested, you can walk 2 blocks to the north and find Fleet Street, which travels east-west across part of London. The Number 15 bus travels east and west on this street, and is an excellent mode of transportation.

The Number 15 bus, if you take it east, will take you to St. Paul's Cathedral and then onward to The Tower of London. You definitely want to see the Tower, even if you only have time to walk all the way around it and see it from the outside.

The number 15 bus, if you take it west, will take you to Trafalgar Square, where you can find the National Gallery and also the National Portrait Gallery. At Trafalgar Square you will find the Church of St Martin-In-The-Fields, which has an excellent cafe in the Basement, Cafe In The Crypt.

To ride the tube or bus you'll need an Oyster card. This can be bought at Gatwick Airport, at Blackfriars Station, or at the Tourist Information kiosk (shaped like a glass triangle) across the street from St. Paul's Cathedral. You can walk to St. Paul's from your hotel; it's only about 6 or 8 blocks.

There is a great restaurant near this Premier Inn. Walk out the front door of your hotel, walk north up Dorset Rise St., to Fleet Street. Look across the street, and to the left. There you will find Ye Olde Cheshire Cheese. Excellent place for food and drink.

There are several different trains you can take from Gatwick into London. One of these is the Gatwick Express, which puts you into London in a different location from the Blackfriars Station mentioned in the above posts.

Gatwick Express puts you in at Victoria Station, which is near Buckingham Palace, Westminster Abbey and Parliament. There is a Premier Inn hotel about one block from Victoria Station.
http://www.premierinn.com/gb/en/hotels/england/greater-london/london/london-victoria.html?cid=GLBC_LKEBAR

From this location, you would have an easy walk to all the sights I mentioned above. You would also be near the Churchill War Rooms, in case you are interested. You would also be not far from the river, where you could walk over Westminster Bridge and along the south bank of the river to Shakespeare's Globe Theatre and the Tate Modern Art Gallery. There are pubs and restaurants along the riverside. A walk along the river or one of the walks given in Rick's London book would be fun.

If you don't already have a map of London, you will want to get a good one to take with you.