Lucerne is a medium-size city, but it's fairly compact, so all sites can be reached via foot. The city can be reached by bus or train. The difference between daytime and nighttime in Lucerne is literally night and day -- during the day, it is a sweet Swiss city; at night people are getting drunk and escort services are available (they are even advertised in tourism books).
There are a few Lucerne hostels (but more budget and upscale hotels) in the city, a couple are within fifteen minutes of the train station. During the summer these Lucerne hostels fill up quickly, so try to book well in advance. Switzerland is expensive, so be prepared to spend more money than in other Western European countries.
There are many sites to see around Lucerne including the Chapel Bridge (also known as the portrait bridge), the Water Tower, the Musegg Wall, the Jesuit Church, the Mill Bridge, the Lion Monument, and the KKL culture and convention centre. The Musegg Wall is free and offers breathtaking views (make sure to wear sunscreen -- it won't seem as though you're burning, but a sunburn appears). On the way up to the Musegg Wall, there are pastures with Hairy Coos (Scottish cows, the same breed as the infamous Hamish in Scotland). The Chapel Bridge is absolutely gorgeous during the day as well as night. The old town portion offers gorgeous paintings of some of the buildings -- wander around the old town and you will undoubtedly find some.
Around town there are multiple grocery stores, food markets, restaurants, shops, and sweets stores (including a well-known macaron store in the old town portion). Additionally, in the summer they occasionally set up flea markets. They often have events going on, including a Red Bull extreme BMX event in town. In addition to the festivals, shops, and sites, do what the Swiss do -- enjoy the lake and parks (swim, boat, barbeque, or hangout)!
This is a safe city; just don't wander around at night alone (make sure you have a friend with you). It is gorgeous and peaceful and should not be missed. In terms of a cheap meal, grocery stores are the best bet. Since most of the sights can be seen for free, the high prices are somewhat outweighed by not having to pay admission fees to sights.
Hi, I'm Kari,
the Hostelz.com local expert for Lucerne hostels. Welcome.