Seeing a play in London is well worth it. As for suggestions, it depends on your interests and the age of your family members. Do you want a comedy, tragedy, serious drama, or big budget musical? Do you prefer a larger theater or a smaller intimate venue?
You can look at What’s on Stage to see what will be available. Also, Theatre Monkey helps you determine which seats to buy based on price, view, location, and comfort.
For something light, I enjoyed “The Play That Goes Wrong” which is hilarious and suitable for children.
Here’s a link to an earlier discussion of this question with more suggestions:
All the best,