I'd just take the Stansted Express train from Liverpool Street, especially given that you'd already be in the area. It takes 45 mins to get to Stansted Airport and trains leaves every 15 mins. The coach services (National Express and Terravision) will save you money, but they take longer, and there's the heavier evening traffic to bear in mind - and you did ask about how to best utilise your time.

So even if you did want to get to Stansted two hours beforehand, you wouldn't need to leave until say the 17.25 train. Liverpool Street station is on the edge of the City and there's plenty to see around there. You could meet your friend for a curry down Brick Lane which is round the corner.

You can make the Stansted Express a little cheaper by buying tickets through the Ryanair affiliate portal here.