[Addick]

As most people will be able to help with the touristy stuff, I'll share some of the cheap and/or day-to-day spots.

Pop Brixton - It'll be cheaper than a sit-down restaurant and hipster pub but it pricey for street food. Nevertheless, it is cool pop-up beer/food hall and has a great atmosphere/vibe.

Southwest London - Richmond and Kingston upon Thames are posh suburbs but they are beautiful river-side towns that show a different side to the city than Central London. It can also be cheap as you can grab a meal deal (£3 for a sandwich/pasta salad + chips/veggies with dip + drink) from a supermarket and sit on the banks of the river. You can also bring a few drinks as you are allowed to drink in public.

Pub Quiz - If you are able to find a pub with a good pub quiz night, you'll be able able to cheaply entertain yourself while soaking up the pub culture with locals.

Thames Clipper / River Bus - One evening, take the tube out to North Greenwich or the DLR to Royal Victoria and the Emirates Air Line (gondola) to North Greenwich. From North Greenwich, take the river bus into central and take in the sights as you speed down the Thames. It has an on-board bar so you can have a cheeky cider.

Food Market - Borough Market is the best food market but it will be full of tourists. Heading to one of the smaller markets would give you a more off the map experience. Either way, do it on the weekend.

A Football Match - It doesn't have to be a Premier League match but it does have to be done. Head down to the ground early and join the supporters at one of the pubs. It is a proper experience and takes place inside and outside of the stadium. Try to get a seat close to where the loudest home supporters sit. It's not dangerous and you'll appreciate what they bring to the experience.

A general piece of advice, you can often easily walk between underground stations. It can save you a few extra quid and you get to see more of the city including some of its hidden gems.