There are so many! I live in Cape Town and I still haven't got to everything! A few places I'd recommend you see or do while here:
1) Go up Table Mountain at sunset or during the day.
2) Visit Robben Island and Nelson Mandela's old cell if you like history.
3) Go to the V&A Waterfront, take a canal cruise, take a tour of Cape Town aboard the Red Bus, shop till you drop, enjoy some of Cape Town's best restaurants.
4) Take a day trip to Hermanus (little coastal village - you can watch the whales if it's whale season, visit quaint coffee shops and stores, etc), or mark a day out for wine tasting along Stellenbosch, Durbanville and Helderberg wine routes.
5) Enjoy sundowners in Camps Bay.
6) Visit the World of Birds in Hout Bay - with over 3000 birds it's one of the biggest bird parks in the world.
7) Have a picnic or enjoy a concert in Kirstenbosch Gardens.
There is SO much more to do!
I recently wrote a hub on Cape Town - it will give you a bit more of a feel for what you can expect on your honeymoon here :)