An electric scooter would be ideal.
Bicycles suffer from a peculiar characteristic of humans, namely that they produce power at a ridiculously low RPM. Power is force times speed. If speed is low, to get any useful power, you need huge amounts of force. The rotational equivalent is that power is torque times RPM, very similar to the linear equation.
Let's consider how much torque a 100 kg rider that pulls up 30 kg from the handlebar exerts. 130 kg = 1275 N. That at 0.17 m crank length is 217 Nm. It's probably more torque than in my car engine!
I don't know what issues you have had with bicycles, but I'm suspecting it may be related to the drivetrain components, such as chains and sprockets wearing out quickly. They do that because of the huge forces involved, due to the low rotational and linear speeds.
Here's some bicycle failures: http://pardo.net/bike/pic/fail-001/000.html -- those occur because bicycles are lightweight and need to withstand extremely high forces.
Additionally, handlebars, stems, etc. can crack due to huge forces involved when pulling up from the handlebars to obtain more force on the pedals.
Also, most bicycles are designed to be easy to pedal. If you have electric propulsion, for example low rolling resistance of tires is no longer a must. Thus, you can have thicker tires that get less punctures. Bicycle tires are designed to be usually low rolling resistance, at the cost of frequent punctures.
Ideal electric scooters use typically smaller wheels for higher RPMs at the same linear velocity. They use a different drivetrain that works at high speed, allowing the engine to spin at 10 000 RPM or so. Electric motors like to spin at 5000 - 20000 RPM, generating very little torque but considerable power due to the high RPMs. Less torque equals smaller numbers of failures.
One answer recommended a 50cc scooter. The cheapest are often two-stroke engines generating very harmful exhaust emissions. Even the 4-stroke ones may lack a catalytic converter (although I was reminded that the best models may have a cat). Actually, the non-catalytic-converter tiny 50cc engines are more harmful than a car engine if you consider only the harmful emissions (they may generate a little less CO2 per mile, though). So, whether a 50cc scooter is environmentally friendly will depend on the exact model: do get a 4-stroke one with a catalytic converter.
I'm sure most places are modern and allow electric equivalents to 50cc scooters. Get such an electric equivalent! Chances are it will eventually save you the amount of money you have to spend on gasoline.
Edit: after this answer was written, I found that one of my workmates has bought an electric unicycle. It requires considerable skill to use, but it's much lighterweight and smaller than a bicycle, and you can carry it wherever you go including carrying it in public transportation. Cost is significantly below 1000 USD / 1000 EUR. Whether you dare to invest in unicycling skills is another question, but it may be a very useful investment.