The easiest way to get to the Warner Bros Studios Tour is to take a train or, if you're not in a hurry, the London Overground (it's the Underground but above ground... uh..yeah) to Watford Junction. At Watford Junction, there's a Doubledecker shuttle bus that takes you to the studios. I think it was £1.50 per person. Takes you directly there. When you want to come back...just reverse your journey. The trip to Watford Junction may cost a bit though ... it's in zone 8 or something like that. I think it cost us £8 one way to get from there to Paddington Station (we used the Overground/Underground because it was snowing and the trains were, shall we say, less reliable. You won't have that problem in June!) We actually took a minicab to the studios because of a snowstorm and we were starting from outside of London. In case you're curious, it was £58 from Slough/Windsor to Watford Junction. We splurged but we're glad we did because of the snow. Train to Watford Junction is at Euston Station. Overground/Underground to Watford Junction is ... well, also Euston but just make sure it's not the train station station.
I assume that you're going to see more in London than just the studio tour so I'd just stay somewhere that's close to the sights and the Underground. Maybe something near Euston. There seem to a few, not many, hotels that have 2 double beds .... I'd book them soon though. I had trouble finding twin rooms for my brother and I at a reasonable price.... hence we're paying a really unreasonable price.