How many of you are going, and what's the age range?
My all-time fave thing to do if the group is all old enough is the London Walks (
www.walks.com) Jack the Ripper tour. They do quite a few other tours if Jack the Ripper isn't your thing.
Definitely do an afternoon tea somewhere. Groupon often has deals on teas. I never manage to book ahead, but you will need to for some of the more popular places.
http://www.afternoontea.co.uk/ can give you info on a lot of the teas.
Museums aren't really off the beaten path, but there are some fantastic museums in London and I wouldn't skip them. I think they are mostly still free for general entrance, though sometimes you have to pay for special exhibits. Combining my suggestions all together, you could easily do a London Walk at the British Museum then hit a nice tea in Bloomsbury nearby. There are a lot of small, specialist museums as well, but I don't know what kind of thing you are into.
My family always make a point of going to a Wagamama to eat (
www.wagamama.com) and Pret-A-Manger for sandwiches when they visit from the US.
There are a lot of markets around London, but I think Camden Market and Borough Market are the most frequented. Borough market is great for food and Camden for, well, just about anything. Oxford Street has pretty much all the shopping in terms of stores that anyone could want.
You can go and watch Parliament in session. It can be less than exciting, but is kind of a neat thing to do.
http://www.parliament.uk/visiting/visiting-and-tours/
You can also do day trips out of London fairly easily, even if you don't want to drive. London Walks does some, but any touristy areas or major hotels (you don't have to be staying there) will have brochures on other companies too. Also, there are a couple of companies that do London tours by bus. Most operate a hop off-hop on service, so you can get off if you want to see something then pick up another bus from the same company when you want to move on.
