Free time in London

Grosvenor Gardens area is very close to Buckingham Palace, Hyde Park, Kensington Park and Palace, The V&A Museum, the Science Museum. And these are just the things that just popped into my head, I'm sure with a goggle search you will/can find many more things depending upon your interests.These alone are enough to keep you busy for 2 days. I would also recommend that you check walks.com the London Walks website and check your dates for walks they are conducting on the days you are in town. No need to make reservations, just meet up at the scheduled spot and pay your money. Have a great trip. I love London.

Are you going to be in those cities on your tour? If so it would be helpful to indicate what your itinerary says you will visit. What do you like to see? History? Art?

You will be near Buckingham Palace, but it won't be open for visitors in June. You can walk thru St James's Park and Green Park. You will be within walking distance of the Guard's Museum along Birdcage Walk and for me it would not be too far to walk to the Horse Guards, Churchill War Rooms, Big Ben, Houses of Parliament and Westminster Abbey if you are not going to do any of those on your tour. There are London Walks in the nearby area. I took one on Wartime London that I really enjoyed but did take the Tube to the starting point, then it wound it's way back to an ending point near the War Rooms. I've walked to all those places I listed from a hotel on Ebury St which is near Grosvenor Gardens.

It is also fun to go to Googlemaps and put in your hotel address with the satellite view, in case you haven't done that already. It will list many of the interesting things nearby.

editing to add: Looks like the "Pam's" are thinking along the same lines and both love London!

As I mentioned for Rome, taking public transport to any popular neighborhood in the city is a very quick trip by Tube, bus, or taxi, so you could easily spend a half day exploring a spot that's nowhere near your hotel. A guidebook is best to know your options, but the free tourist maps given out by hotels also have all the main sites marked, as well as the tube stops. A self-guided walking tour is again a great way to see the city center. London Walks is also a recommended guide service, or you could do a cruise along the Thames, if you don't think those overlap with your other tour plan.

The MUST see spots for first time London visitors are nearly all within walking distance of each other. As another OP suggested use the Google Satellite option for London. Type Big Ben London United Kingdom into the search box and you'll see what we mean. Big Ben, London Eye, Parliament, Westminster Abbey, Horse Guards, St James Park, Churchill War Rooms, The Palie, and Trafalgar Square are ALL reasonably close to one another. Personally, I'd include the Tower of London, Leadenhall Market, and St Paul's. All close to one another in the City of London neighborhood. Merely a tube ride away from Grosvenor Gardens via a District or Circle train from Victoria to Tower Hill. See the Tower first, then the glass covered Leadenhall market and finally over to St. Paul's. From there meander toward the Thames and the Blackfriars tube station. If you are into enjoying a pint in a truly lovely setting visit the Blackfriar Pub directly across from the Blackfriars Tube station. Can't miss it. Art Deco gem. The chicken and mushroom pie is outstanding if you'd care to dine there as well. http://www.nicholsonspubs.co.uk/theblackfriarblackfriarslondon/

All of the above locations fit the must-see list but it should be noted that public transport in London is not an obstacle to overcome. Indeed, get on the Tube and you are half an hour from the vast majority of the city's most important sites.

The nearest attractions to your hotel are Buckingham Palace, Westminster Abbey, Houses Of Parliament, and (walking over Westminster Bridge) the London Eye, and Shakespeare's Globe Theatre. You are also within walking distance of Covent Garden (lots of restaurants, pubs) and then from there to the British Museum. London transportation is swift, so don't think that a trip on the tube or bus is going to take a chunk out of your day. For that reason, I've included a full list of "must do's".

1. Westminster Abbey
2. The Tower of London (do it first thing in the morning to avoid crowds)
3. St. Paul's Cathedral
4. The British Museum
5. Take a Hop-On-Hop-Off bus tour for a two hour ride by all the major sites, so you can get an overview (with an announcer telling you what you're passing) and decide what you may want to see next. Some sights are adequate with a "drive by" if you have a limited amount of time in London. Your ticket is good for 24 hours, during which time you can ride, hop off to see a sight, and hop back on the bus, as many times as you like. Your ticket includes a boat ride on the River Thames. The London landmarks are interesting to see from the river view.

That's my top five. If you are still not out of energy, then look at these.
6. The Museum of London (Detailed history of London from the Roman times onward)
7. V&A Museum
8. Go up in the London Eye
9. Shakespeare's Globe Theatre
10. Tate Modern Museum (for modern art)
11. National Portrait Gallery (for portraits of famous Brits, including the Tudors, Henry VIII, and more)
12. Hampton Court Palace (Part-Tudor palace where Henry VIII lived, very short train ride out of town, but worth it.)
You won't have time for all of these, but pick and choose from the list. Get a good map of London, and you will see several parks that you may enjoy near your hotel. Have a great trip!