I paint on site, sitting where I can and trying to stay out of the flow of people. I use light-weight, portable paints and paper - normally hardback sketchbooks from Saunders-Waterford and tin watercolor boxes.
The emphasis is on portability and speed of use - there's something special about capturing a scene in one sitting. My focus is on the building so you'll sometimes see areas barely sketched in, if they're not the main focus I'll just put enough detail in to keep the shape of the scene.
I tend to use one paintbrush, one simple box of paints and either a fountain-pen or dip-nib with a bottle of ink. My Saunders-Waterford sketchbooks are traditionally bound, so in every book I will have several double-spreads where I can use the whole width of two pages, and just unstitch the thread later to release the whole sheet, as in this painting of the interior of St Barts near Smithfields in London.
I carry all of this in a shoulder-bag, with a small, collapsible stool as well. The heaviest thing is often the water, as I do like to be able to refresh it a few times.