Gordon Ramsay Restaurants
Probably Claridges Hotel for the set lunch (£35 plus drinks and tip for a few choices for each of 3 courses). He won't be there of course, but it has his name, it's great value, it will proably be busy and it's in a good location. Sometimes they offer quick kitchen tours. My teenagers love it.
Petrus might also be OK.
The flagship in Royal Hospital Road can be a bit hushed.
Not going to ask 'why Gordon Ramsay?' but none would be my first choice for the brief.
It depends to some extent on whether the key point is wonderful room/service or whether it is the food and if so whether you are looking for interesting or just classical.
Maze: modern interior, quirky food.
Claridges: average food but beautiful room and service as you'd expect.
The 3* restaurant: decent (expensive) and fine for a well-behaved 13-year-old but at that price there are better options.
If you wanted to expand happy to advise more.
Personally, I'd take my 13 year old (I do have grandchildren near this age) to Bread St. Kitchen. I haven't eaten there, but it sounds a lot less stodgy than some of the other choices. I think your foodie will enjoy it. I haven't been to Maze since the previous chef left, but it's a fun restaurant with things that are certainly 'different.'