Geneva is right on the shores of Lac Léman (Lake Geneva), so it's quite lovely to walk around and explore. A boat cruise of the lake and river, and a walking tour or explore of the Old Town as a starting point. Check out here for more info - www.geneva.info/tours The history of La Vieille Ville, Geneva's Old Town, can be traced back 2,000 years. It is where you will find many of Geneva's most interesting attractions and sites like the Barbier-Mueller Museum, the St. Pierre Cathedral (for CHF5 you can go to the top of the cathedral and the views are more than worth it), the International Museum of the Reformation, The Art and History Museum and the Tavel Mansion. It is one of the largest Old Town's in Europe. The Old Town is built on a hill side south of the Rhone River, and has picturesque narrow meandering cobble stone streets lined with historic grey-stone buildings which now hold boutiques, sidewalk cafes and restaurants.
The United Nations is a great place to check out too, and you can get there through the Botanical Gardens, either walking or biking, or catch local buses. There are also free bikes that you can hire and explore all over the city (you just need to take them back within 4 hours, easy!) you just turn up with CHF20 cash, no need to pre-arrange it, check it our here - Free bikes.