Great... what are they striking about, and what are the alternatives for tourists?
They're striking for increased pay and guaranties of job security.
Assuming that the strike isn't called off - the alternatives for tourists (and every one else) are basically everything else. The strike is only by tube drivers so overland trains, DLR and the buses will still be running and there is always a taxi or mini-cab. Obviously these will be a lot busier than usual and traffic will be worse so allow more time for your journey and try even harder to avoid rush hour.
Here's a press release from TFL:
http://www.tfl.gov.uk/corporate/media/newscentre/11971.aspx
they (and all of us)should be happy they have jobs at all!
Political commentary aside; if you are travelling in London the TfL journey planner under "more options" has the facility to (de)select the type of transport options used. Unticking "Tube" will give alternative transport options.
If the tube is closed, the streets will be a madhouse and even worse at rush hours. The buses will be packed and will be creeping slower than you could probably walk...I can't remember if it was a strike or a breakdown or what. but the tube wasn't running one evening I was there and I was almost late to a show because it took an incredibly long time to get across town. I sure hope you don't run into this problem.
Stay in a central area and walk as much as possible. Sometimes the buses block the streets in gridlock and don't move even when the Tube is running. The Victoria area is walkable to Buckingham Palace, Whitehall, Trafalgar Square, Leicester Square, the theatre area and that entire city center.
When there was a strike in Milan, I went sightseeing on the Hop on/Hop off bus. I was lucky I was walking distance to these buses! Using the hop on hop off bus during a strike was great! I barely noticed there even was a strike! Use these in London!
The strike is only June 9th through to the 11th.