I have lost count of how many paper cups I've ridden past on my way to everywhere just in the past week. These cups cannot be recycled due to food stains, and the waxy coating they often come with.
Klean Kanteen makes an excellent thermal mug that fits in a water bottle cage. It comes with a loop cap, or you can buy a sip-top separately. Its $30 price tag will pay for itself in just weeks of daily use; and it will keep a hundred or more paper cups out of the landfill in six months or less. (A Klean Kanteen figures prominently in my Coffeenneuring photos.)
Join me in reusing your coffee mug! And maybe we can see less of this on the roads.