How to see London off the beaten path?

I doubt there's much of anything you won't find in a guidebook as London is one of the most written about cities anywhere.  For places off the main tourist track, some of my favorites:

• Eltham Palace, about 20 minutes outside central London by train, decorated in the art deco style
  
• Freemasons' Hall, access is limited so be sure to check their website for opening times
  
• Sir John Soane's Museum, the last time I was there they were offering tours of the private apartments by reservation only, see if that's still available
  
• Leighton House Museum
  
• Museum of Brands, Packaging, and Advertising, might still be closed, they were moving shortly after my last visit, fascinating look at advertising organized by major event like weddings and coronations and wars
  
• Regency Cafe, hardly a secret anymore but for me it's a must for breakfast
  
• Mrs Kibble's Olde Sweet Shoppe, stop and get clove balls every time I visit
  

Also don't overlook places like the British Museum or V&A just because you've been, often they have excellent special exhibits like David Bowie or ones on fashion at the V&A or the Terra Cotta Warriors at the British Museum

Obviously, it depends on what sort of thing you enjoy doing in a big city, but I can give you a personal recommendation based on what I get up to in London as a local.  

I live in East London and there's plenty to do in this part of town.  

Brick Lane, Spitalfields Market, Redchurch Street and Shoreditch are great places to spend on the weekend. It's vibrant and busy, full of great boutique shopping, street food and street art. People of all ages and backgrounds, tourists and locals hang out here. If you like Indian food, check out Dishoom! Or head to Kingsland Road for Vietnamese food - choose from twenty something Vietnamese restaurants on this road alone. It's easy to get to on the Overground.  

Sundays you can catch the Columbia Road Flower Market. People from all over London go there to buy flowers and plants, drink nice coffee and eat nice cakes.
www.columbiaroad.info  

See what is playing at Arcola Theatre and eat gorgeous Turkish food in Dalston. You might even bump into Gilbert & George at Mangal 2 (I have!)
If you're into nightclubbing, Dalson is the place - Dalston Superstore, Dance Tunnel...
https://www.arcolatheatre.com/
http://www.whataplan.com/plans/show/65/share-a-kebab-with-art-legends-gilbert-and-george-in-dalston

If you ARE East, The Geffrye Museum is free and doesn't take long to walk through. 
http://www.geffrye-museum.org.uk/

And the southbank is always a great place to hang out. Hayward Gallery tends to have cool exhibitions, see live shows at Royal Festival Hall.
Or just get some food from the Sunday Food Market and sit on the Thames and watch the sunset.  

The Hackney City Farm is always good fun to walk through on your way to London Fields, which has a market in Saturdays. And then walk along Regents Canal towards Victoria Park. You can see all the amazing canal boats along the way. Speaking of canals, it's also quite nice to take a canal tour boat from Camden. It's lovely, especially as the boat heads west, and exciting going through all of the locks! 
http://hackneycityfarm.co.uk/

Horniman Museum and Gardens is something different too! 
http://www.horniman.ac.uk/

I suppose this is a good start. If you have more specific things you are interested in, say so, and perhaps I can help.

Go look for Abbey Road... entirely underwhelming, but fun. Go to 222-B Baker Street to the The Sherlock Holmes Museum. Take the train to Greenwich and stand on the Prime Meridian. They have an excellent museum there, too. Plus, it's a pretty place to walk around.

Hi Katja!

Since there are so many guide books on London I guess that my favorite places are surly included in some of them. ;) Anyhow, here it goes:

• Electric Cinema - cute cinema with a luxurious feel. Think 1920s living room. This is really an experience! Check out the pictures and get ready to be amazed.
  
• Mitre - old, classic English pub that's kept lots of the decor from 1875. Lots of beers to choose from and the food is also good. Cocktail bar in the basement if you're up for that.
  
• The Fan Museum - I haven't been there myself yet but it's on my list. A friend of mine was there last summer and said that it was really cute. Also, they offer afternoon tea. 
  
• Liberty & Co - old department store with an impressive christmas decoration section (open september-december) as well as other amazing stuff.
  
• Pho - Vietnamese food. Tastes great and not that expensive.

Also, I enjoy just walking around in Soho with all the shops, bars and other things going on. I always visit at least one museum. On my last visit to London I went to The Sherlock Holmes Museum (small but well-done) and The British Museum (yes, I know that you already know about that one. My favorite there was the cat mummy in the old Egyptian section). I also recommend to catch a Broadway show if you are into that. Have a great time in London!

Portabello Market is fun as is the Camden Lock Market

Hi Katja,

Walk or cycle the Thames Path it's a really interesting way of seeing many of the London sights from a different perspective. I have only walked one part of the path (From Tower Bridge) but there are various trails - all the way to Oxford Checkout this website: https://tfl.gov.uk/modes/walking/thames-path

If you love coffee, head to Great Titchfield Street. A hugely fun spot is The Attendant which is a cafe underground in a converted Victorian-era public toilet. The coffee and snacks are great, there's free wi-fi and it's not far from the main shopping precinct around Oxford Circus if you're looking for a bit of R&R