Arriving Lucerne by train late afternoon on Friday, October 3rd, and planning to stay until Monday. We would appreciate any budget priced lodging referrals for the area. If the referral is for the area around Lucerne, please suggest methods of transportation to and from the city as well as suggestions of must see's and do's. Thanks much.
You might start with Trip Advisor/Lucerne and check out the list of Lucerne hotels. They will be listed with an average room price, and you can see reviews from previous guests. Lucerne, as well as most of Switzerland is pretty expensive.
Check out Backpackers Lucerne. It's a hostel but they also have private rooms. A double is €49. It's about a 10-15 minute walk from the train station. The hostel is situated on the lake and is very clean and staff is friendly.
I can second Jennifer's recommendation for Backpacker's Lucerne. We only stayed there one night -- it was extremely clean and very quiet, and the location was convenient. I stayed in a double room with my daughter, and we had a balcony that overlooked a pretty grass courtyard with big trees.