You can just hop on the trams and buses but if the inspectors arrive they come in force, and it is very hard to slip away.
Accommodation & Wild Camping
There are many hidden spots along the river where somebody could camp out for a night or a couple if the weather is nice.
If you go straight down from the Hirschengraben (close to the train station) following the tram-tracks, you will find a small park on the right side after a few blocks. It's a good place for sleeping out, but by the river is much better.
You can camp in the Stadt Nomaden or stay in someone's caravan if you ask for a couple days. It is located in Studerstein (a park) Directions: once you reach the park you can ask this name. It is a little area bordered with fences, where there are caravans and many dogs. To come to the park, you can take the bus 11 direction Neufeld from around the city centre and get off at the last station. There you will see the Studerstein and the forest, don’t go into the forest :)
There is an emergency sleeping place called Sleeper, where you can get a bed for 5.-, breakfast included. But they only accept people in an emergency, not people who actually could afford a hostel bed. Check-in times are from 10pm-1am and you can stay till 10am. Be there soon enough, especially in winter time. You can't make reservations.
Shower & swiming
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Monday-Friday at Aufenthaltsraum, Postgasse 35. Opening times 8.30-11.30am with free breakfast, and 2.30-5.30pm with free coffee, tea,... Postgasse is located in the lower old town, close to the (bus #12 stop) Rathaus.
There is also a Bakery (with attached vegetable-shop) which sells Sandwiches, Bread etc. from yesterday (they collect it from Bakerys in the City) and because its from yesterday they sell it for the Half of the Price. Its located in the Celler at Marktgasse 19 and the Name of the Shop is "Ässbar", open Mo-Fr. 9-19 and Sat 9-17.
Tuesday-Friday and Sunday at 12.30pm at La Prairie, Sulgeneckstrasse 7. It costs 5 CHF, if you can't afford that you can work for it in the kitchen. From the main trainstation go to the park "Kleine Schanze", on the right side of the park there is the street Sulgeneckstrasse and La Prairie just 50m from there.
Every day from 6pm-8pm at the Sleeper. It costs 5 CHF. The place is located at Neubrückstrasse 19. From the main train station, walk towards Bollwerk/Reitschule. Go behind the Reitschule building, cross two streets and you will see it. Bus 11 or 21 stop there, the stop is called Henkerbrünnli (which means Hangman's spring).
If you need to use a Computer for a shorter time: visit a Library. The most of them have Computers free to use but limited in time (1hr or so), but you can always ask to extend. In the National-Library ("Nationalbibliothek", Tram #8) you just need to ask the Person by the Computers (not the person in the entrance) for a Code.
There's a free internet café at Monbijoustrasse 16. Follow the tram lines of #9 south out of the center and find the Internet Cafe Power Point on your right hand side. The place is just for the unemployed and poverty-stricken, but if you're a penniless traveller, they'll likely let you use one of their machines for half an hour. (Never mention you are a traveller, hitchhiker or whatsoever)
Alternatively, there also is a free, publicly useable computer with internet at the Autonomous School at Lagerweg 12. From the train station, go downhill towards and past the well-known alternative culture center Reitschule, cross the bridge, turn left and turn right. Open most days around 6-8pm, and at other times.
you don't need a permit. but the competition is pretty intense and almost all the streets have cars so there are very few great spots for the un-amplified buskers. but according to some you can earn 50-100 francs in an hour or two. according to others you can expect more like 10-40 in a couple of hours.
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