I’m probably not the best person to advise on the tourist sights, but London does a very good job at cramming lots of recognisable sights into and area that can be covered on foot.
Decades since I went to the Tower of London, but as a child it amazed me how much was there
The museums and art galleries are seen as a great bargain, and some are still free to get into
The changing of the guard was of more interest than I expected it to be.
I always forget whether it’s the Tate Britain or Tate Modern that has the Rex Whistler restaurant. Apparently the food is decent without hitting the heights of the specialist restaurants, but the wine list is where there is huge choice and sometimes a screaming bargain.
Covent Garden often has a good buzz in the evenings, and whilst it’s a bit touristy, it’s not extreme, with a mixed bag of street performances.
I love my food, so Borough Market is often a destination - pricey at times, but there is some very good food there, from Mini Magoo’s granola, through fine cheese shops (including a branch of Neal’s yard), great olive oils, cured meats, olives, etc. The coffee at Monmouth’s is very good, though there is rarely the space to sit down. Lots of other good food places (and much rubbish in the tourist areas). Getting a picnic together at Borough Market (nr. London Bridge tube / station) might be nice even if staying in a Hotel. The other great place for a picnic, is an awfully authentic Italian alimentari on Old Compton St called ‘I Camisa’. Inexpensive but great pasta / fresh pasta sauces, and plenty of other stuff in a cosy and simple shop. If you’ve got an apartment, this is where I’d shop on a budget if I still wanted really tasty food. Across the street the ‘Vintage House’ is one of a number of places in London with a good Whiskey selection, and just a bit further on is the excellent Algerian Coffee Stores for very good coffee beans & loose tea. Piccadilly circus is often a convenient tube stop.
Shows are very much not my thing (more like torture), though I know Wicked gets good press. Look to others for your advice here!
Try to plot to walk whenever possible, and buy an A2Z map as soon as you can. Many visitors walk further to get a tube 2-3 stops, than they would if they simply walked directly there. The tube is often a grim soul-destroying experience. Buses are better, but find a good app to help, as most people find it too confusing to work out the routes. ‘Oyster Cards’ are a decent option even for just a few days. A friend also speaks highly of the river ferries, especially on a nice day, and if your travel plans are up/down the river.
There are a few enomatic tasting wine bars around now. The Sampler is good, but both are a little way out of the way - handy if heading in that direction.
Rochelle Canteen is getting some very positive feedback on Wine Pages, as the adopted home of the ‘Oddities’ tastings. It’s an old school bike shed near Liverpool St Station, converted into a modestly fitted out restaurant. BYO on the wine - I can’t remember the corkage, but not excessive. The only catch is poor glasses & whilst bringing your own is ok, not especially convenient if travelling.
I agree on the parks - a wonderful asset, often under-used. On a nice day, they make a good picnic destination, and are great for an early morning walk.
As with any major city, if you have a special interest, London will have a shop for it, and it’s well worth preparing in advance. Try yell.co.uk for the business listings, and the site is easy to use.
One ‘mustn’t do’. I had to endure ‘The London Dungeon’ one year with relatives. If you love appalling ham acting in stupid sets, then it might appeal. Otherwise you’ll spend your time wondering if there is a side door to sneak out of.
Hope this helps
Ian