One of the best cites I would love to roam any day and would never be bored of visiting the place again and again. The heritage buildings and parks are very well maintained. The transport network is excellent and impressive. Grab a free map at any of the metro stations and a day ticket which entitles you to free rides for a day – http://www.wienerlinien.at/wl/ep/home.do?tabId=0 and dont forget to punch you cards on the machines avaliable at the entrance of each metro platform and near the doors of a bus or a tram. You can also use free internet accessible at roadside kiosks.
You can check into a decent room at Wombats Hostel – http://www.wombats.at which also has a wonderful kitchen & a pub on the ground floor.