Lucerne is a centrally located and a beautiful little town.
We stayed for seven days in Lucerne and had a seven-day Euro Pass to enable us to travel by train from Lucerne to all parts of Switzerland (a Swiss Pass is normally ideal).
Our itinerary was as follows:-
Day 1: Reach Lucerne, around noon, check-in at the hotel, explore the town in the late afternoon and evening.
Day 2: Reach Lucerne station by 7am, take the train to see Mount Titlus--a must for first-time visitors to Switzerland--return in the late afternoon and spend the evening around the lake in Lucerne.
Day 3: Take the 7am train to Geneva, pass beautiful countryside and vineyards en-route, and spend about six hours seeing the city's international organisations and lakeside with the beautiful fountain. Return by the 5:30pm train to reach Lucerne around 9:30pm.
Day 4: Visit Mount Pilatus and spend the rest of the day shopping and relaxing in Lucerne.
Day 5: Take 6:30am train to Interlaken and then take the private railway up to Jumffroh Glacier (around US$75 per person)--wow, what a tour; it's just out of this world. Return back by 10pm.
Day 6: 7am train to Zurich, with a stop first to see the largest falls in Europe, Rhine Falls--extremely small on a worldwide scale, but still worth seeing. Reach Zurich by noon and spend the day going around the city and lake side. Don't miss out on the boat ride on the lake--it's a must.
Day 7: Some shopping in the morning and check out by 1:30pm.