To say it simply: The Tate Modern Museum is worth the price of admission and more (since it’s amazing and it is free).
To say it more complexly:
I sometimes struggle with coming up with activities to do when people come to visit since London is massive and almost has too many options. Also, speaking selfishly, I don’t want to do the same things every time I’m hosting someone who visits me. The excellent thing about London is that UK museums are (mostly) free and there are so many of them that I can choose which ones to bring people to.
The Tate Modern is great because the featured exhibits are changing and even though you need to pay for them, it is fun to see what new trends are occurring in the modern art sphere. The exhibits that are here to stay are thought-provoking and exciting. My favorites are ‘Babel’ by Cildo Meireles and ‘The British Library’ by Yinka Shonibare.