Annecy is indeed lovely - but not easily accessible without a car.
There are many lovely places that are though - like Yvoire on the French side of the Lake which you can get to by boat - or Montreux, easily accessible by train.
Edit: just checked on the Swiss train website www.sbb.ch
(you can click on English version). It seems that you can get there in 1.50 mins BY BUS rather than by train. Go on the website, type a date and departure time, and they will give you all the options.
Or perhaps ask if someone on EF would like to join you, and offer to pay for petrol and lunch. You never know.