Hope your bike is fitted out for commuting, with lights, fenders, and tough slick tyres, depending on the weather or conditions.

Small first aid kit in a 2x3"ziploc bag with antiseptic wipe, sterile dressing pad and a few sticking plasters. Mainly to treat road rash.

A small pencil and paper to write down the number plates of cars.
Some form of id and home address. Public phone box card or coins, emergency cash (for spending on a taxi or booting a split tyre). I dont rely on there being cash in my wallet at all times.
In a big city, I usually carry a map or street plan and a button compass. Seriously, have you ever tried navigating on a dark night.

I swapped the puncture kit for a few Park self-adhesive patches and sandpaper, but I haven't mended by the road for years. Use the kit at home. On jorneys over 10 miles, I carry a mini Leatherman, the one with pliers and a double folding handle.

Keep a spare gear and brake cable (they are different) at work. You can probably finish your journey without them.

I always find a couple of plastic bags, a zip tie and some pvc tape (wrapped around the frame) come in handy.

These days I keep emergency spare socks, Tshirt and underpants at work, in case I forget to bring them in.

I alwyas seem to carry to much clothing, but our weather is very variable and unpredictable.
Michael