There are a number of threads discussing what tools guys here carry on their bikes. Do a search for Tool Kits and Tools in the search box, right end of the blue bar atop this page.
Basically they range from a credit card and/or cash up to a full Snap-On tool chest worth of tools. It's really up to you. Basic stuff would include a spare key (in your wallet), tire kit - compressor, tubeless tire tools and fresh gummy worms and cement, and you take it from there. Guys on bikes like yours might carry a spare fuel pump (aftermarket) and tools to replace that. Ditch your philips screwdrivers and get a set of JIS screw drivers (Japanese Industrial Standard - looks similar to a Phillips but allows more torque w/o destroying the screw head). What exactly would you want to do on the side of the road or in a parking lot while on a trip? If your battery is ageing, 4 yrs old or older, you might carry a lithium jump start battery with you or change your battery before you leave home.
Don't forget the RAN (Rider Assistance Network) list - blue band again, Riding > U.S. RAN List. Print it out. Better than any tools.
If you do regular maintenance, like changing fluids as Honda recommends, and plan ahead, you should not have maintenance issues on the road. When I say maintenance, I also include preventive maint - such as changing the tires before a trip, etc. It really depends how far you will stray from home and how often. Talk to
@Uncle Phil and ask him what he will be taking on his cross country trip this June.