I get a fair number of requests from people coming to London for the first time, as well as some repeat visitors who want to know where to start to plan their visit. I always recommend the Visit London web site.
First Time Visitor
They have a whole section that look at what it will be like when you come to London for the first time. (The Link is here).
Especially good is their section on Getting Around London which goes in to detail about how tubes and buses work, as well as what tickets are best value based on your plans. They even direct you to mobile apps you might think of downloading before you come, or once you are here if you have free WiFi in the hotel. They also provide information about the London Cycle Hire Scheme, although the price for this has increased substantially in recent months.
There is also a month-by-month planner which lists some of the special events occuring in each month for the next year – everything from the Notting Hill Carnival to the Queens Birthday.
Many London museums are free and the planner has a list of these here – a good way to work out what you might be able to do cheaply.
If you bringing the family there is a page for what to do with kids in mind – planner is here. Especially good is the page on Harry Potter sets in London.
Repeat Visitor
If you are coming back then you may find the area suggestions helpful, to enable you to explore somewhere you have not been before.
Covent Garden is a fairly obvious place that you may have seen before, if so why not try somewhere new like Richmond and Kew, the City of London or look at upcoming events in the next few weeks.
Another page that you may find useful is the London Icons – check you’ve seen them all.
For everyone there is lots to do in London and with a weak pound no better time to come and see this great city for yourself.
If you have specific questions please post and I will do my best to answer them.
One thing I regularly do when going away for longer periods of time, and one thing I’d wholly recommend people to look at before coming to London, is daily deals sites. Tourist tickets always tend to be close to the list price, and if you scope out Groupon, Living Social, Wowcher, etc before traveling you could happily get some good deals/discounts.