Hello Again,
I don’t think any hotels in London will be cheap during August but the Premier Inn is a good chain. Their County Hall hotel (there is also a Marriott on the same site but their prices are a bit scary!!) is in a very good location but gets booked up very early. Be careful when checking their website and check out the hotel locations on a map as their idea of London can be quite a long way from the centre. (Travel Lodge is also a reliable, but more basic, chain.)
1. we'd love to go on the Harry Potter Studio tour
This is just outside London. You can get a train from London, Euston to Watford Junction where you can get on a special shuttle bus to the studios. (You will need to buy your Studio Tour Ticket online as you can’t buy them on the door.)
https://www.wbstudiotour.co.uk/plan-your-visit/getting-here
2. see the Tower of London
Quite expensive but very, very interesting. Make sure you have a “Beefeater” tour as it is included in your ticket. Food here is expensive and not to my fussy kids’ taste.
3. ride on the Eye
I’ve not had the nerve to do this! Great reviews (Right next to County Hall hotel)
4. spend at least one day just wandering (hopefully that is a safe thing to do) eating, having a beer (me only of course), shopping, chatting with some locals
Not sure how many locals you will find in London in August. I’ve always felt safe walking around – take normal big city precautions agains pickpockets etc. You might find this website interesting
http://www.londonforfree.net/walks/
5. Sherlock Holmes museum
I’ve not been here, but it gets good reviews.
6. an art/culture museum (open to suggestions)
Plenty of choice in London. Most are free. Most have children’s trails/activities if you ask at the info desk.
My favourite is the V&A
http://www.vam.ac.uk/page/t/the-collections/ (not too far from Harrods)
The National Gallery
http://www.nationalgallery.org.uk/ in Trafalgar Square (walkable from County Hall)
7. Big Ben, Parliment, some castles (I'm a huge Henry the VIIIth junkie), changing of the guards
Big Ben is the bell inside the tower that we usually know by that name. (Opposite County Hall)
Hampton Court Palace is 30 minutes by train from Waterloo (the station near County Hall). Probably the easiest train journey you can make as each end of the line is a terminus station. I have been here many times and can easily spend 5 or 6 hours here listening to the audio tour and the many costumed guides. (Again food expensive but you could take a picnic and eat it in the gardens.)
http://www.hrp.org.uk/HamptonCourtPalace/
8. take our photo at Paddington Station (the kids are Paddington fans)
9. have fancy tea somewhere (we just don't have anything like that here, and I'd love for us to experience it)
My friend took me here for my birthday
http://www.langhamhotels.com/en/the-langham/london/dining/palm-court/
Very expensive but absolutely wonderful. I’m sure there a plenty of other locations in London.
10. maybe see Stonehenge if it is possible without having to rent a car and drive (I'm not sure England needs me trying to drive over there!!!)
Lots of companies run trips here. Not a lot to see to be honest. Maybe combine it with a trip to Salisbury a beautiful town with a cathedral.
11. see some Shakespeare
You should be able to do this at the Globe, Barbican or national theatre, depending on their summer programmes.
12. check out a library there just to see it and compare, maybe see a movie while we're there too
The British Library is more of a museum than a regular library
http://www.bl.uk/
I used to use Holborn Library when I worked in London
http://www.camden.gov.uk/ccm/naviga...earning-centres/holborn-library/?context=live
(It’s not far from The British Museum)
Happy Planning.