There are three main reasons why you should take the train to visit other cities on the shore of lake Geneva (alternatively you can also take the boat which I did from Vevey to Montreux, but in the majority of other cases, train might be a better option):
1. Train rides in Switzerland are super scenic - lake and vineyard views guaranteed.
2. The connections are really good (trains depart every couple of minutes from Cornavin) and the trains are quite fast (provided you don't hop on the train that stops in every town).
3. It's more sustainable than a car.
You might argue that taking the train from Geneva to Lausanne is expensive (indeed trains are no exception to the rule in Switzerland) (although to be honest travelling by train can be quite afforable with half-fare cards), but if you book a day or two in advance and specify the exact time of departure, you can get the supersaver tickets which can save you more than 50 % of the original price even without having the half-fare card (also, I really recommend using the SBB app because it's super easy and fast to book a ticket with it).
There are numerous spots that are easy reachable from Geneva by train and definitely worth visiting, but if you're on a tight schedule, you might want to consider these:
Nyon is an incredibly charming and underrated little town situated on the coast just 20 minutes outside Geneva. Walk through the narrow streets of the old town to reach Chateau de Nyon with incredible views over the town's rooftops and the lake and continue your walk from there through the tree-lined avenue to reach Porte Ste-Marie, ruins of a majestic Roman gate.
Colourful facades and a mighty old hilltop cathedral - supposedly Switzerland’s most impressive piece of early Gothic architecture - are two of the many reasons why it's worth spending an afternoon (or two or three) in Lausanne. Sports fans will enjoy Musee Olympique, while party animals will be interested in one of the many bars and clubs the city's famous for.
This lakeside pearl is especially worth visiting in September and October, when it hosts an international photography festival Images Vevey. The whole city turns into one big interactive gallery.
If you're interested in more exciting getaways from Geneva, read all about hiking Le Môle.