In the past few months, I've put up over 1300 miles cycling. Gyms closed, so I was not able to do my normal routine of strength training. I had bought a road bike a few years ago and I lived in the Bay Area, which meant lots of trails and very good weather.
After my second week, I had a flat and realized I was not prepared at all. I made a list of things you should carry in your bike bag.
If you don't have a bike bag, I recommend this saddlebag. It's cheap and gets the job done.
Always bring a spare or two! I recommend the Continental Race Tubes. I have tried different brands and they have always got a hole. I haven't had an issue since I've been carrying these in my bike bag. Make sure you get the right valves and stem length.
CO2 Inflator and Canister
You can always bring a bike pump in your bike bag, but the CO2 inflators are so much cooler. I ended up buying this Lezyne CO2 inflator because it has a control valve. You will need to bring some canisters in your saddlebag.
One time, I hit a bump so hard, but handlebars dropped. I highly suggest you bring a multitool with you. You never know when you need a last-minute seat or cleat change. I have a Park Tool bike multitool, but you should find one that matches your bikes nuts and bolts.
The wife and I each carry a $20 bill in our bags.