Hey there!
You don't mention budget for your accommodation but I can suggest afew..
Backpackers
Long Street Backpackers - clean, has a bar, brilliant location, can get a private room
Ashanti backpackers - slightly more on the fringes of city centre but quieter. Again it's clean and can get private rooms.
Hotel
African Villa in Tamboerskloof in the suburb beside the city centre is really nice but it usually needs booked in advance as it's popular but as we're out of the tourist season you may get lucky. Here's a link to info, pics and booking online. It's R490 pp per night. A bargain for what it is.
http://www.capestay.co.za/africanvilla/ Obviously there are the usual hotel chains but I haven't or don't know anyone who's stayed in them to recommend any others.
I hope you have an amazing time in Cape Town it's an awesome place!
Lou