I am a bit of a West End geek and have seen pretty much all of them. I wouldn't go for the Disney ones really. I thought LK and Frozen were fine, but not in the same league as the ones below. Most of the big musicals are great nights out, but some are just on a different level.
Four shows stand out for me amongst the current shows, but two of those four are ones that I would definitely recommend for a first timer.
The four are...
Six. I found this funny, clever, poignant, and very sassy. But it is short, and more of a themed concert than a musical, I would say.
Operation Mincemeat. This is very cleverly done with a small case all playing multiple roles. It's a true story and the songs and choreography are great. It's the funniest musical I have seen yet there is one song that had me absolutely bawling crying. But for some reason it lacked the epic nature of my other two recommendations below.
Hamilton. As others have said, this is absolutely astonishing. I am no lover of hip hop but the staging, songs, lyrics, choreography here are our of this world, and as a set piece it is definitely the best I've seen. Jaw dropping. A definite tip would be to listen to the songs beforehand and get to know them. That way you can appreciate all the rest of it. The emotion in the second half is stunning.
Les Mis. I think this might be my number one. I have seen it half a dozen times and each time I am struck in different ways by the story, the songs and lyrics. Some of the tunes and sentiments stick with me for years afterwards. It is an incredible piece of work. Beautiful, tender, inspiring, astonishing.
I hope you love whichever one you choose.