1. In Switzerland

Gruyères, is an amazing walled medieval village with a castle, and which blends the medieval with the modern – it has the Giger museum and bar (Giger is the creator of Alien, the cinema character), and also a beautiful tiny Tibetan museum. Reviews are available on http://www.tripadvisor.com/Tourism-g1...… It is about 2 hours from Geneva, or 2 1/2 hours via the very worthwhile http://www.goldenpass.ch (Routing: Geneva - Montreux - Montbovon - Gruyeres).

Lausanne is the second largest city on the Geneva Lake and is – unlike Geneva – a very “Swiss” city.  It is not all that easy to find your way around as it occupies a long, sloping hillside down to the lake which is cut by the old riverbed of the Flon, making it hard to see on a map exactly what level you need to be on!  See this link for more information about Lausanne - http://www.tripadvisor.com/Travel-g18... The Lausanne cathedral is the finest example of the Gothic style in Switzerland and a visit there also provides a terrific view of the central (and widest) part of Geneva Lake.

Vevey is about 15 minutes from Lausanne by train. When leaving the station walk towards the lakefront and you will find yourself on the huge Grand’Place or Place du Marché where there is a large local market on Tuesday and Saturday mornings.  In summer the Saturday market is particularly big.  From the Grand’Place walk towards the lake and into the old town – la vieille ville. This is very extensive and is full of lovely 18th century buildings, little boutiques and small cafés. There are several museums in Vevey that are “different” from the ordinary…  The Alimentarium, housed in a beautiful “hôtel particulier” on the lakefront is a museum of Food. Then there is the Museum of the “Confrérie des Vignerons” which is a wine growers association that holds ‎ an elaborate pagent once every 20 years or so (www.fetedesvignerons.ch). The next “version” of this will happen in the summer of 2019. The museum is in the old town and gives all sorts of information about the association, the pagents it has held and the reasons behind them. There is also a fine art museum in Vevey, the Jenitsch, which has changing exhibitions and a good permanent collection.  

In warm weather you can go to the beach at la Tour de Peilz for a swim and a lovely view on the French Alps on the other side of the lake.  Or take the funicular up to Mont Pelérin for great views over the city, lake,mountains and Lavaux vineyards - with the option of walking back down through the latter  (with stops at caves for wine tasteings or at  the tearoom in Chardonne)

If you want a longer walk in the area you can hike from Mt Pelérin to Chexbres (or take the train there from Vevey station) and then have an even longer walk down through the vineyards to Cully or Rivaz or St Saphorin all of which villages have train connection back to Lausanne and Geneva).

Montreux is nice too, with the famous Chillon Castle http://www.chillon.ch/. About 1 hour from Geneva by train. To get to Chillon you can either take a bus from the centre of Montreux (10mins) or a lake boat (15mins).  Buses run every 20 minutes or so and you pay on the bus.  Do get an Audioguide at the entrance to the castle as it will greatly add to your enjoyment of your visit and your understanding of the castle.  And allow about 2 hours to visit it.  From Montreux you can take a train up to the Rochers de Naye (1 hour) where in summer there is a marmotte park and at Christmas time you can meet Father Christmas (!)  The view (on a clear day of course!) from the top is wonderful.  You look over to he French Alps and the Mt Blanc range and down to the Lavaux vineyards as well as to the Valais alps to the south.

Martigny is a small town in the Valais with a beautiful old centre and a stunning Place Centrale.  It is dominated by the Château de la Bâtiaz and is home to a world class museum, the Fondation Gianadda.  For more information about Martigny see this link:  http://www.tripadvisor.co.uk/Travel-g...

Bern, the Federal City (there is no such thing as a capital city in the Swiss Constitution) is really worth a visit. For more information on Bern see http://www.tripadvisor.co.uk/Travel-g.... Direct train ride from Geneva takes less than 2 hours.

Extending the travel time to 3 hours allows one to go further, notably to Zermatt, Interlaken or Lucerne. But 6 hours in the train might be a bit too much in one day...

Geneva Lake – with a rented car it is possible to make a complete circuit of the lake in one day.  For a route and places to stop on the way see  http://www.tripadvisor.co.uk/ShowTopi...

 

2.  In neighbouring France

Yvoire: Go by boat (in Summer, it is worth it!) or by train plus boat via Nyon (1 hour for the latter option, a but more for the former. You can walk around this lovely walled village, visit the “Jardin de Cinq Sens” – a garden which offers you the chance to smell, see, touch, and taste the flowers and to hear birds singing.   The village is full of small boutiques and galleries and should you wish to eat there it has a really good (Michelin listed) restaurant just outside the walls called “Le Pré de la Cure”. Their speciality is Filets de Perches, the famous local lake fish, which they serve in a lemon-butter sauce with home made pommes frites! Wonderful. For great value choose one of the “menus” at the back of the menu offerings. In 2012  the cost for a three course meal here, with “amuse bouche” to start with and “mignardises” with your coffee was 35.50€ per person, service and tax included. Reservations are recommended on the weekends… +33 4 5072 8358  

Chamonix-Mt Blanc and the Aiguille du Midi (3842m above sea level): One hour by car or more, either by private transfers or by public bus (details on http://www.gare-routiere.ch/ -> drop-down menu on the bottom right of the page -> select "Alpine resorts" - buses leave from "Place Dorcière", behind the English Church on the rue du Mt Blanc or from Geneva Airport)..  See the Chamonix Tourist Office site for a list of companies offering bus and transfer services - http://www.chamonix.com/taxis-shuttle... - but be careful!  One of the companies gets consistently poor to bad reviews on Trip Advisor and it pays to check on the Switzerland Forum pages when making your choice.  The most-visited place in Chamonix is the Aiguille du Midi – you get  up there by cable car - and affords amazing views of the Mt Blanc and the Chamonix valley as well as the famous "Needles" that tower above Chamonix.  Be warned though that the last several minutes of this ride are almost vertical up the cliff face and if you have any fear of heights at all don't go up!  Once you are up there you can also experience their "newest thrill" which is walking onto a totally transparent platform with a drop over over 1000m below your feet.  Again not recommended for those afraid of heights!  You can also take a train to the "Mer de Glace" a glacier near Chamonix.  On Saturdays there is a wonderful market in the middle of town.  The views of the Mt Blanc and the glaciers coming down it are breathtaking even from the centre of town.  An excellent place for lunch - outside in good weather - is the Maison Carrier which is right across from the market square.  They offer a series of "menus" at various prices from about €18 to 30.  A three course meal there including the "plat du jour" and a wonderful dessrt buffet will cost you about €25 not including wine and coffee.  They have a lovely garden which is a perfect place for an apéritif in summer.

Annecy, also in France and also easily accessible by bus from the Gare Routière in Geneva - details on http://www.gare-routiere.ch/ -> drop-down menu on the bottom right of the page -> select "Alpine resorts" - buses leave from "Place Dorcière", between Geneva main train station and the lake, or from Geneva Airport)  -   is another lovely place for a day trip.  Annecy has a beautiful old centre, with river running through it and sits on the lake of the same name.  Boat cruises on the lake are a good thing to do on a warm, sunny day and meandering around the old town in Annecy is a great experience.