Once you have settled in to your accommodation your first challenge is to climb Table Mountain and get a broad picture of the place. Fortunately there is a cable car going up to the summit which makes life easy. However there is no point in going up there on cloudy day when the "table cloth" is set, for you will see nothing. Watch the weather and pick your fine day. A mini-cab will take you to the cable car terminus, and a little further on to the Kloof where the hiking track starts, if you are that energetic. Details are given in my Bootsnall article Table Mountain
Mementos to take home? Obviously nothing bulky. I always check out the textiles and traditional fabrics to buy as gifts for friends. Wall hangings, table cloths, table runners, scarfs, sarongs etc are often brightly coloured, and clothing items made from traditional fabrics. Jewellery made from beads and shells are worth inspection.
Cape Town is a fun city to explore. You wont be disappointed and will come back time and again to relax amidst wonderful beach and mountain scenery.