The most fuel efficient motorcycle in my collection was running about 75 mpg. Not bad but I new I could put together an inexpensive "rat bike" that would be fast enough for commute and get over 100 mpg.
Started with an old Honda Trail 90 that I bought 15 years ago for $75. It ran then but died and was retired to the pile of old bikes in the back 40. Engine was too expensive to repair so I bought a new Lifan 110cc engine for $235.00 including shipping from Hooper Imports. 2 new street tires and an air filter from JC Whitney for $60. Forks were bent so I put on a set from an XR100 dirt bike. Second gas tank from the XR100. Head light $6 from Harbor Freight. Tail light is a trailer light $5 from Walmart.
The bike has no ignition switch, just a kill button. No battery, lights work off the magneto. No steering lock. A $8 bicycle speedometer. It's as simple as I could make it. It's also UGLY (on purpose). No one is going to steel it even though they could just get on a ride away.
The bike has a top speed of about 50 mph and rides very well. It's licensed and insured. Holds over 3 gallons of fuel in the 2 tanks for a range of 300+ miles. Should last a long time with the brand new engine.
I had a moped in college. I totally BMXed it out, knobbies, BMX bars, grips, pedals and covered with stickers. I loved the speed bumps on campus. I'd hit them full speed and do no-footers and can-cans. Damn the bastard that stole it from my storage unit.