Taxi's are a good way to get around London (expensive, but as long as the taxi is genuine then it's better than walking round late at night). Make sure you use the London Underground- cheap, efficent, and fast. And you get to check out the locals in all our quiet glory as every local uses the Underground here.
As a few other answers have suggested, I wouldn't go to a restaurant if you don't want to spend too much money but instead, there are many nice deli's or shops you can pick up cheaper food from. The best places to get sandwiches, pasta, wraps etc. are supermarkets: Sainsburys and Tescos do some good pre-made stuff, and they only cost a couple of pounds.
However if you are looking for a restaurant, London has some great ones. I recommend Launceston Place in Kensington, it's not too pricey and it's good a traditional British menu and the few times i've been there, i've never been disappointed. A chinese noodle bar called Cha Cha Moon in Soho is really cheap. Alot of restaurants add a service cost to the bill after everything has been ordered- a bit cheeky. Otherwise, go by how much you liked the meal. If it was crap, don't leave anything. If you loved it, give them loads. How the system should work. And a must is to try fish and chips- there are so many fish and chip shops in London, make sure you grab yourself a portion. Another nice idea is to have a full English breakfast one morning, every single cafe serves it up.
As you're a first time visitor, you'll probably want to see all of the typical sights of London- London Eye, Houses of Parliament, Westminster, Buckingham Palace. There are many museums and art galleries if you're into that sort of thing, and alot have free admission.