It is quite acceptable to use the pronoun "it" since you were asked a direct question and there is no confusion about what "it" refers to. It is a much more efficient sentence than repeating the word "museum" again. Another note: If the word "keen" is a word that you plan to use regularly, I would say that it is a rather old-fashioned word (at least in American English). I can't think of a single person in the last half-century who might use it the way you wrote it. Most everyone would understand it, however.

Yes, it's possible to use 'it' to refer to a gerund phrase 'going to museums', but not ideal. The response is correct, but a little unnatural-sounding. A simpler response, such as 'I love it' or 'I really like it' would be more common. Not that there's anything wrong with using 'to be keen on', mind you. Just to give a perspective on the English language beyond the (admittedly vast) borders of the USA: The expression 'to be keen on' may be rare in American English, but that is not the case elsewhere. In the countries that don't use American English - Britain, Ireland, Australia, NZ, S.Africa - this is a common and widely used expression. You will almost certainly come across it in any English language material from these countries, including coursebooks and English exams. In fact, 'to be keen on' is frequently tested in exams.