Geneva has a reputation for money and diplomacy, and that's the wrong way round to start. This is a city that spent the 16th century as the capital of John Calvin's Reformation, so strict that it was nicknamed the Protestant Rome, and that only joined the Swiss Confederation in 1815. The banks, the watchmakers and the international organizations all grew on top of that stubborn, serious, slightly puritan base. It was also where the Red Cross was born and where the League of Nations, and later the UN's European headquarters, settled in.
It's a small city on a very big lake, with the Jura on one side and the Salève, the mountain locals call their balcony, on the other. The Old Town takes an afternoon. What takes longer is the rest: the Carouge market, the watch museum, the UN, CERN, the vineyards of Lavaux an hour away. Five days is the right length because it lets you do the city properly without hurrying, and still leaves one full day for the lake villages and one for a mountain view. It's also an honest warning about the bill: Geneva is one of the most expensive cities in Europe to eat in, and one of the cheapest to learn things in, since several of the best museums are free or pay-what-you-wish.
Day one is the Old Town and the Reformation, day two Carouge and the museums, day three international Geneva and CERN, day four a day trip to Lausanne and Lavaux, and day five the lake, the Jet d'Eau and Mont Salève. Start on a Tuesday: on Mondays the Museum of Art and History, the Red Cross Museum, CERN's Science Gateway and the Olympic Museum are all closed. The plan also works as a base for the wider region, which is why it points to the Switzerland country page and to the French Alps guides at the end.