In practice the vast majority of NX services into central London only serve Victoria Coach Station. There are other stops much further out (e.g. Stratford) and a few services call at Marble Arch or, for example, Embankment or Waterloo stations but most won't.
(If you want to see where those other stops are go here and enter the postcode SW1Y 6HP for Jermyn Street:
https://www.nationalexpress.com/en?find-my-stop=yes . I doubt that it will help you though, as the service you're using into London probably won't call at any of them. Further, none of them are significantly closer to Jermyn Street than Victoria CoachStation is anyway.).
It's a mile and a half from Victoria Coach station to Jermyn Street. You can break the journey up by walking to Victoria Underground station (inside the National Rail Station), hopping on a northbound Victoria Line service for one stop to Green Park and then walking from there.
By bus you could walk to Victoria Bus Station. [NB: That's not the same place as Victoria Coach Station! The bus station is immediately in front of the Victoria (National Rail) Station]. Then take a 390 bus for just 3 minutes to Hyde Park Corner station, followed by a 13 minute journey on a 14, 19 or 38 bus to Piccadilly Circus. It's a short walk from there.
Notes:
1. Jermyn Street is quite long. It might help to find out whether your destination is at the Green Park end or the Piccadilly Circus end, possibly requiring you to teak the information above a bit. The TfL journey planner can be used to help you. (It recognises the names of theatres, etc):
https://tfl.gov.uk/plan-a-journey/
2. You can't use cash on London buses and you'd be mad to buy a paper ticket for a short hop on the Tube. Just use a contactless debit card for either type of journey.