What is their budget please, and requirements other than commute, are they wanting a 'cool' area with lots happening, or somewhere quieter and more suburban, do they want to be on a tube line or are they happy walking/cycling/getting bus to work - avoiding tubes and trains can be a huge saving of several thousand a year on travelcards so worth bearing in mind?
At 21 most people would be into house sharing with others of the same age to save money and hopefully make friends? Even house shares in London are pricey but popular areas would be to the east of central London, starting in Old Street/edge of Islington areas which would be walking distance to the city, and moving out east to Canonbury, Dalston, Hackney, Hackney Wick types areas, all very popular with youngsters and a do-able cycle ride or short bus ride away - but commensurately pricey and possibly out of reach of some!
If they are on more of a limited budget and/or want somewhere a bit more suburban or quiet then they can easily look further out on the Central Line or the overground trains which go direct into Liverpool Street, places like Forest Gate, Leyton, Walthamstow, Wanstead are nice easy commutes to the city and a bit more affordable than the zone 1 areas. There are also lots of new developments around the old Olympic Park so Stratford and surrounds is more popular than it used to be and has great transport links and also the new-ish Westfield for shopping and amenities. Or you can also look at stations on the Northern line as Moorgate is about 5-10 mins away from Liverpool Street although this would tend towards the fancier/pricier areas like Belsize Park and Hampstead. Basically an awful lot of London will be 30 mins away from Liverpool Street so s/he will have plenty of choice if that's their only criteria!