The Tate Modern is a gallery rather than a museum. I went there once or twice on school trips many years ago, but I am not particularly keen on modern art, so wouldn't choose to go there for pleasure. The one thing I remember about it is the great long Turbine Hall used for large installations, which looks quite impressive when looking down at it from the balcony above.
I was in London in '68 & '88, & went to the Tate twice, & found it most enjoyable, but that's because I love art, so yes, it certainly is worth going too! In '88 2 uni students were selling, MIRO t-shirts outside the gallery/museum, so I just had to buy 1, even though it only came in a big size! (I still wear it sometimes, when I'm out walking!)