Able-bodied travellers will find Lucerne a complete joy to get around in on foot. The Old-Town is tiny, and most other interesting sites are within 20 minutes or so walk, there is also a city bus system (http://www.vbl.ch/), as well as assistance for disabled visitors on request from Mobility International Switzerland (http://www.mis-ch.ch/). The Lido beach and the Swiss Transport Museum are a bit further out and can be reached by bus or by one of several boats per hour from just in front of the central railway station.
Lucerne also makes a very good base for discovering the rest of Central Switzerland, using the Swiss Federal Railway (http://www.rail.ch), the Schifffahrt Vierwaldstättersee (http://www.lakelucerne.ch...), or any one of several private rail or boat companies.
Bicycles are available for rent at the central railway station, at ticket window 21 on the lower level. For 31 CHF per day, you can rent a 24-speed, sturdily-built bike with a baggage clamp. Electric bikes are also available. Bike pick-up and drop-off are around the left side of the train station, at a kiosk across the street from the Swiss Post building. Bike lanes are present on most secondary streets, and Lucerne drivers are generally aware of and polite towards bicyclists.
By bus
Lucerne has an efficient bus network: Verkehrsbetriebe Luzern (http://www.vbl.ch) German only. It covers the city and the suburbs.