Backpacker accommodation and campsites are available at Penduka, which is in Katutura, Windhoek. The Lonely Planet for Namibia and Botswana mention Penduka but only as a place you can buy local crafts (which you can) but actually in my opinion it's the nicest place to stay in Windhoek.
Contrary to what the Lonely Planet suggests, you do not need a guide in Katutura: it felt completely safe.
Dorm rooms are N$110 (or N$150 with breakfast) although I didn't actually check them out. Camping is N$50pp. Good (free) wifi internet is available (as you'll probably be the only guest there, you'll be the only person using it) and it's a beautiful location on the lake.
The only problem is that it's a bit out of town (I think it's N$19 each way in a taxi) but it's an ideal location for travellers with their own transport.
As a comparison: the two other backpackers in Windhoek are Chameleon and Cardboard Box. Neither of which I can recommend. Camping is N$80pp at both of them (which, in my opinion, makes the taxi fares to Penduka worth staying at Penduka). I tried to stay at Chameleon but ended up leaving because the staff were amazingly arrogant and unhelpful. I stayed at Cardboard Box for a few nights and it's really dirty and loud.
Parking at both Chameleon and Cardboard Box is scarce. You have to pay for the wifi at Chameleon; and although it's free at Cardboard Box, everyone's on it in the evenings so it's rubbish.
Incidentally, there are some interesting crafts out at Penduka. Everything is made by women who otherwise couldn't get work (e.g. deaf etc). It's not the same old imported-from-Kenya African tourist junk that you normally see. You can also buy crafts made in Penduka at the Old Breweries Craft Market, which is in central Windhoek.