The South Australia Visitor & Travel Centre can supply information on B&Bs and homestays around the state. Satellite or cable TV is rare in South Australian hotels, though some provide pay-per-view movies.
Plan Ahead -- If you plan to be in town during the Adelaide Festival, make sure you book accommodations well in advance. The town can be packed during Christmas and New Year's, so it's wise to book well in advance then, too.
In North Adelaide
This suburb across the river is an interesting place with nice architecture and good restaurants. It's about a 10-minute bus ride from the city center.
In Glenelg
I'd recommend, without hesitation, staying in Glenelg rather than in the city center. The journey to the city center by car or tram takes less than 30 minutes, and the airport is less than 10 minutes away. Add to this the sea, the lovely beach, the fun fair (amusement park), the great shops, the good pub, and the nice accommodations, and you have a perfect place to relax on your holiday.