DW and I spent a week at the Westin Cape Town without a car in November and never once felt the need for it. You'll be fine without one - not worth the hassle.

You can do a guided tour to get you out to the Winelands (who wants to worry about drinking & driving anyway?). I'd also recommend a guided tour for Cape Pointe and the drive along the coast - gorgeous.

DW & I are walkers - if you don't mind a few mile walk you'll be within an easy distance of the V&A Waterfront, Sea Pointe Promenade, and a walk through downtown to check out some of the shops / food on Long Street. We even walked from the Westin to Lion's Head base and then did the hike up & down. In retrospect we probably should have cabbed that one

As mgn2000 pointed out the Red & Blue bus passes are great. You can get around and see most of "must sees" in Cape Town on those 2 bus lines (Table Mountain, Kirstenbosch Gardens, etc). Definitely worth picking up the pass there - we really enjoyed that and found it invaluable to get out to some of the sites. The busses have pickups right outside the Westin. The 2 day pass can also include a Sunset Ride up to Signal Hill - we caught that on a perfect day and had a gorgeous sunset - if the weather cooperates consider that as well.

We also rented bikes one day from the V&A to help get around. We used the bikes to get the ~5 miles out to Camps Bay, spend some time at the beach, and eat lunch / happy hour at some of the restaurants with great views there. Make sure to make it around Camps Bay & Clifton.

Hope you enjoy your time in Cape Town! Very gorgeous city - one of my favorites