With regard to the possibility of seeing a show (at a sensible price), please ensure that your friends are aware of the TKTS booth in Leicester Square, which is the official Society of West End Theatre outlet for unsold 'on the day' tickets to plays and musicals. They also now sell tickets online, here:
https://officiallondontheatre.com/tkts/
You'll see from the website that some tickets are being offered for today's performances of popular shows, such as Get Up! Stand Up! (with the music of Bob Marley) from £22.80, Jersey Boys from £23.80, Phantom of the Opera (from £42.30), Mamma Mia! from £18.50, etc.
There are a multitude of pubs and bars with live music within central London and around it but, unlike most other cities, your friends shouldn't expect to find many without some sort of entry charge (and booking in advance is often necessary too). These links might help:
https://thenudge.com/features/the-best-london-bars-with-live-music/
and
https://www.squaremeal.co.uk/restaurants/best/best-bars-and-pubs-for-live-music-in-london_16