London - Portebello Road Market
 

Is this something to do on a Saturday morning? What area is it in?

Yes, take the tube to Notting Hill Gate and follow the crowds.

Yes, take the tube to Notting Hill Gate and follow the crowds. Go early.

Make sure you get there early to avoid the massive crowds. Bring cash too...
Afterwards, you can walk to the Kensington Palace/Garden. It's not too far from the Portebello Market area. You can have lunch along the way or have a picnic at the garden.

Do you suggest that we do this on Saturday morning? What else near there can we do for the afternoon sightseeing? Kensington?

The market stalls are on Saturday morning - so if you are interested you can only do it on Saturday. And when people say "early" they mean EARLY - 5 or 6 AM is not too early. You will be done by 10 AM. After that it is simply too crowded to see anything - or even walk comfortably. So Portobello Rd does not take away from any other sightseeing, since nothing else is open at that time of the morning.

As for what to do afterwards - you can do/go anything/anywhere you want. If you don't want to walk through the park, go to Kens Palace, or wander the shops of Kensington - just hop on the tube and be anywhere else in London in a matter of minutes.

The market is only open on Saturday. When you've had your fill come back to the tube station. If you turn right you'll find a Burger King for a potty stop and further along a Europa market.
I can't remember whether they sell sandwiches but you could get other things for a picnic: cheese, bread, beer.

There a number of restaurants but they might be crowded. The famous Geale's fish restaurant is one block on the south side on a street parallel to Notting Hill Gate.

If you turn left you'll come to Kensington Gardens, a pleasant walk to Kensington Palace. Then you can continue to Kensington High Street (and the tube) or, if you're up to it, along Kensington Road to Royal Albert Hall behind which is the Science Museum, Natural History Museum and the V&A.

Of course, you could just get on the tube at Notting Hill Gate and take the Circle Line to South Kensington and the museums.

You can have a very full day.