CERN is one of these international organisations, but it is the only large one which is not exclusively diplomatic and administrative. At CERN we do high-energy physics experiments.
The United Nations European Headquarters occupy the buildings which were once the seat of the League of Nations. Almost all countries have a Mission to the UN in Geneva. Note that neutral Switzerland is not a member of the United Nations.
Geneva is the capital of the Republic and Canton of Geneva, which is one of the 25 states (cantons) of the Swiss Confederation.
The city is divided by the river Rhone. CERN is on the right bank, the old part of the city is on the left bank. There are numerous bridges and a few islets. Geneva has a little over 150'000 inhabitants, the entire Canton has 340'000, spread over 282 km2 (somewhat bigger than the centre of Paris, smaller than Lake Tahoe).
Despite its size, the Canton still has rural areas: there are quite a few vineyards which have improved remarkably in the last few decades.
The classic Geneva landmark is the single-jet fountain in the harbour, which reaches up to 150 meters.