By effort
Short and rewarding. Lion's Head. The spiral summit, about two hours up and down with a short scramble at the top (chains and staples; fine in dry weather, avoid in wind). The best city-and-ocean panorama for the least climbing. India Venster is the quiet alternative if you want fewer crowds and a real scramble.
Half-day. Table Mountain via Platteklip Gorge (the direct, safe, boring way up; take the cable car down) or Skeleton Gorge from Kirstenbosch (greener, steeper, through forest then onto the top). The cable car runs in good weather only; check before you commit to a one-way hike.
For views without the climb. The Pipe Track along the base of the Twelve Apostles. Flat, an hour or two, ocean the whole way. The best walk on the mountain for someone who doesn't want to actually climb it.
The mountain, specifically
Table Mountain is not a hill. People get lost and fall on it every year, and the weather on top can be a different season from the weather below. The "tablecloth" cloud that rolls over the summit is a real weather event, not a mood. If it's in, the cableway is shut and the top of any hike is in cloud. Pick your day, and check the SANParks weather alert before you commit.
Before you go
Take water, more than you think. The top is windier and hotter than the bottom. Tell someone your route. Start early to beat the heat and the cable-car queue. And don't hike the quiet routes alone. Lion's Head in mid-morning on a weekend is the social, safe version; the back routes alone at dawn are not.
The cable car, in one paragraph
It runs when the wind allows, which is most summer mornings but not all of them. Buy tickets online to skip the queue. The queue to go up at mid-morning can be an hour; the queue to come down in the late afternoon can be longer. The move is up first thing, down by ten, or up late afternoon for the sunset and down in the dark. If you're hiking up and cableing down, check it's running before you start, or you're hiking back down Platteklip.