Best way to get around is by bike. There is nextbike (bike rental) in Augsburg. Also you can use the tram. Tickets range between 1,35€ up to 13,00€. Normal price is 2,70 €. There are not many ticket inspections so you could try fare-beating.
To get further away you can hitchhike. http://hitchwiki.org/de/Augsburg
- If you are willing to pay some money, try https://www.airbnb.de
- there is the Grandhotel Cosmopolitan
- Main Train Station: Located in the center and always open is the main train station. There is a small waiting hall and a few benches on the platforms (outside). It is common to find some people resting in the waiting hall and tolerated by the Deutsche Bahn security guards as long as you don't intend to crash there for more than a single night. If asked, just tell them you wait for a train that leaves early in the morning and they usually leave you alone.
Meet fellow travellers on hospitality exchange networks: Trustroots
There is free WLAN on to big places in Augsburg: Königsplatz and Rathausplatz. Also in the Information Office and in some trams and buses. If you are connected to edoram you can us Internet at university and FH (Haunstetterstraße). Some user are providing free Internet via Freifunk. http://augsburg.freifunk.net/info.html