We are going to talk about what you should have in your repair kit. This is a basic repair kit with a few nice things to have in it in case you get stranded you will be ready to go.
You definitely want to have a pump. This is a really popular Morph Pump. Basically what it does is it will morph out and become a floor pump so you can get a lot of pressure in your tire. It actually has a gage on it. There are also smaller pumps out there and different styles but you definitely want to make sure that you have a pump so that you can pump up your tire.
A lot of people carry around tubes. You can also carry around just a patch kit. Sometimes the hole is too big that the patch kit will not work, but if you are in a city there is usually a bike shop pretty close so you can just carry a patch kit; you do not have to carry a full tube.
It is also nice to carry a little bit of cash in your kit that is separate from your pocket cash so you can actually use the dollar bill for patching a tire or you can use it for buying a tube or a tire lever or whatever, if you forgot yours.
Also, make sure to have a couple of tire levers; maybe two or three. It is usually good to have three just in case you break one and you need two to get your tire off.
It is also really nice to have a pair of gloves in your kit just because if you are going somewhere you do not want your hands to be super dirty. It is really hard to get grease off your hands if you do not have the proper soap, so that is really nice to have.
It is also really important to have a multi-tool. This is a really nice multi-tool that will have your Allen keys, also known as hex keys, screwdrivers, a chain tool just in case your chain breaks. This is a toe strap for pedals. It is really nice to use to cinch down things if something fell off your bike or to even cinch down your shoe to your pedal if you have clip-less pedals and clip brakes. So this works really well. It is kind of like the Duct Tape of the bicycle world.
And then just have a rag just to make sure that you can wipe off your hands, wipe off your chain or just if something is on your bike that you need off.
So that is a really basic toolkit that you need for the city. You could obviously put a lot more or you could obviously take away a few. This is just the one that I use around the city and it seems to work really well.