Should we stay near Victoria station or would you recommend a better location?
There are plenty of excellent locations to use as your base in London. We have often stayed at the Thistle Hotel (I think now called the Grosvenor) inside the Victoria train station. Very nice (not inexpensive though), and a good location with plenty of shops nearby for getting snacks, etc. and good restaurants and good transportation options. Covent Garden/Neals Yard is also a favorite of ours. The Trafalgar Square area is often mentioned on this site, as is Earl's Court. London's sites are not all grouped together. You will be using the tube or buses and walking some. So find a location with a tube and/or bus stop within easy walking distance and the price range of hotel or other accommodations that you want. Generally if you stay within Zones 1 and 2 on the Tube map, you will be close enough to get to most sites easily and not spend lots of time traveling.
As I mentioned above we like to be able to pick up evening snacks and prefer to have a grocery store or news shop or similar that has cookies (biscuits in Brit speak), cheese, crackers, chips (Crisps) and sodas, bottled water or juice available. We also prefer using the Tube to buses (just personal preference) so we stay near Tube stops.
Victoria would be a good location for general sightseeing purposes. Three Tube lines meet there, giving you good connections to other parts of the city. There are good rail connections to Canterbury and other day-trip options south of London. There's bus (coach) service to Heathrow and Gatwick. Some of the tour companies you might use to visit other places outside London start from Victoria. It's walking distance to Westminster Abbey, Buckingham Palace, the Tate Britain, Harrod's, and other places you might want to visit.
London sights are so spread out that there's no ideal "central" location for general sightseeing. You'll be using buses or the Tube no matter where you stay. You might prefer a quieter neighborhood like South Kensington or Notting Hill, or many others. Rail stations like Victoria are busy crowded places, and so are their immediate surroundings. The Rick Steves guidebooks to London and England suggest several hotels near Victoria, which many posters on this board seem to like -- I can't speak from experience.
London is expensive, and it may be tempting to look for a hotel or apartment in the suburbs. But that means you'll spend a lot of time, and some money, going back and forth each day. Better to stay in London itself. You'll get good (mostly) advice here if you can share some info about your lodging budget, sightseeing interests, etc.
I would add that some places may look fine on a map but when you are there it's either unattractive or even kind of dodgy/unsafe. For example, one day in spring 2015 we headed for London Wall / Museum of London / Barbican area, only to find it was a huge noisy construction site at that time with jackhammers, dust curtains, orange netting andconcrete barriers all over the place. We weren't staying overnight, but even an afternoon's visit was like "get me out of here!" A short walk south to St. Paul's Cathedral and everything there was just fine.
So, read the guidebook to identify areas of London that truly interest you -- which we did -- but also make inquiries about any temporary conditions. We flunked the second of those!
There's lots of construction around Victoria at the moment due to reconstruction of the tube station and redevelopment.
Thank you for all the great information. This is daunting but I am greatly appreciating all the advice.. please keep it coming!