If you are talking day time wandering a bit i think central like bree street would be fine. But cape town is not a "wander around" at night city. And never has been. As a born and bred Cape Townian I can tell you we havr always been ridiculously anti walking anywhere except up Table Mountain! South Africans are often a weird juxtaposition of active and outdoorsy with "drive from.shop a to shop b, 100 m apart! "
Staying in the waterfront is the most likely to give you that sense of just wandering out whenever you feel like it.
I have been enjoying insta posts from secretcapetown - might be worth checking out.
Things I like doing when I am home (although dont do all of these as much these days with dc!)
Lunch in Hout Bay. I used to love Dunes for the perfect view but not sure if its still there.
Kirstenbosch. I find it astonishingly relaxing. The Sunday evening concerts might have started by the time you arrive so worth checking out. But I always visit kirstenbosch at some point and the kids now love it too.
Pottery painting - i think its in hout bay too but will check.
Markets - there are a few but you will have to check where and when. Kirstenbosch and Hout Bay used to be lovely. There might be in observatory or Woodstock.
The world of birds
Cricket at Newlands
Afternoon tea at the Vineyard Hotel
Go swimming in the palmiet river. This one might not be entirely advisable if you are travelling alone.
Spa and massage at 12 Apostles hotel.
Walk up Lions Head - find a group or tour.
Kalk Bay- a great day out with lovely boutique shops and lots of cute little arty cafes and restaurants. We used to take the train but I am not sure if thats a great idea these days. So uber or drive.
For shopping, the waterfront feels too overwhelming! My local was Cavendish Square and I still have a soft spot for it - explore just outside and in surrounding streets too. At Constantia Village the main mall is a bit pointless but I have always liked the little add on bits.
Breakfast at the buffet at the Raddisson in the Waterfront.
Rhodes Memorial has glorious views. But it might be shut to visitors as I think there was a fire.
Take a walk along sea point promenade (by day). Just filled with locals exercising, socialising, being, and its goegeous along the sea front. There's also a sea water / tidal pool there somewhere.