Hi
@Deb in IA
Sorry, this is going to be a long reply, but I wanted to give you some of my hints & tips!
Most of the trains to London I have been on have places to stow luggage on each carriage, as the trains usually have tourists on board, the trains seem to be well catered for luggage.
What area of London are you looking to stay in?
My favourite place is the South Bank, right beside the Thames, because you are so close to all the big attractions and sights - London Eye, London Aquarium, London Dungeons are all in very close proximity. There is also a Thames Clippers dock beside the Eye - these are the boats that sail up & down the river, with stops along the way. There are stops beside places like Tower of London & HMS Belfast.
Further along you have the OXO building, the Globe theatre, HMS Belfast, The Shard, London Bridge, and across the river the fabulous Tower of London.
A stroll across Westminster Bridge (beside London Eye & County Hall) and you are at Big Ben, Houses of Parliament, Westminster Abbey & Westminster Tube station. Walk along Whitehall to see the Cenotaph, 10 Downing Street & The Churchill War Rooms, Horse Guards and St James' Park. A walk through St James Park, or The Mall which is beside it, will take you to Buckingham Palace.
There is a
Premier Inn (hotel) located in County Hall, which is the curved building directly behind London Eye, but there are a large number of other hotels within the area. Most hotels will have joining rooms (two rooms connected to each other by an internal door). That might be an option for you?
For renting somewhere, try
http://www.homeaway.co.uk were owners advertise there properties for holiday rentals.
I would recommend looking into a Visitor Oyster card (for use on the tubes & London buses).
http://www.tfl.gov.uk/travel-information/visiting-london/visitor-oyster-card
There is plenty of info & a video (I think!) on the site, but you basically top-up/load money onto the card, and tap it against the big yellow dome at the tube station gates & bus doorways (a bit like tapping your magic band against the mickey heads at the rooms, park entrances etc)
The tube is incredibly handy & you get used to it pretty quickly. Apps like CityMapper are great for putting in you location & destination, and CityMapper will recommend which tubes and/or bus routes you need. It will move you around London faster, so you can take in a few sights at your own pace.
For the hop-on/hop-off, look into The Original Tour London Sightseeing -
http://www.theoriginaltour.com (sorry for again referring back to County Hall, but they have stops beside it!)
Another tour I would recommend is the London by Night tour. We did it a few years ago when I took my DBF on his first trip to London - and loved it! We got some lovely photos of iconic sites like Big Ben lit up -
https://londonbynight.com/london-by-night-sightseeing-bus-tour.htm
For HP, some travel involved in this.
http://www.wbstudiotour.co.uk
We have never been, but it is meant to be brilliant, and is definitely on our to do list. I have taken the travel info direct from the website:
"The Studio Tour’s nearest railway station is Watford Junction and direct services arrive there from both London Euston (20 minute journey) and Birmingham New Street (1 hour journey). Other non-direct train services operate from London Euston, but please be aware that these may take longer to arrive at Watford Junction.
A shuttle bus, operated by Mullany's Coaches, runs from Watford Junction to the Studio Tour with a journey time of around 15 minutes. Please plan to arrive at Watford Junction 45 minutes before the time stated on your ticket and have your ticket or booking confirmation ready when boarding the shuttle bus."
I have never been to StoneHenge, but from the website it is 9.5 miles away from the nearest station (Salisbury). While you can get a direct train from Waterloo to Salisbury, you would need to look into a taxi or bus for the rest of the journey. There may be a coach that runs direct from London Victoria Coach Station.
Westminister Abbey's website provides times of all its daily services, as well as when special services are being held.
http://www.westminster-abbey.org/worship/general-service-times
My recommendations would be London Eye, Tower of London, Westminster Abbey, St. Paul's Cathedral, The Churchill War Rooms, walk along Whitehall for 10 Downing Street & Cenotaph. Walk along The Mall to Buckingham Palace. If its good weather on a Sunday afternoon, sitting along the South Bank people watching & taking in the different street performers.
Hope this helps!