For years (33 to be exact), I've kept mine in my wallet, along with the other insurance cards of the vehicles we have. That's why is so darn fat I guess. Although, under the seat is most practical. I guess I've never pondered beyond my wallet. That's a good thing (Martha Stewart).
There's a storage space under the seat, intended for your owner's manual. I placed a little bag in that space, next to the battery, for registration, an extra set of contact lenses, an extra set of ear plugs and a $10 bill for gas.
I do the under-the-seat thing on the R3 and the Bonnie but I do a fifty like Tomo says. I also have AMA MoTow which covers out of gas and certified towing and flat tires as well as minor mechanical things (nuth'in on the R3 is minor, however). It also covers our cars and pickup truck and on the cars it covers lockout (I'd never do that but Amy might ) and tire changeout. This ain't a plug for the AMA or MoTow.
I could practically carry 5 gallons of extra gas on the Bonnie as the sidecar has a 5 gallon auxillary tank, but I have never used it. The R3 has the leather bags but under the seat where the owners manual goes is more secure and out of the weather.