I bike to work in Japan, where we still have lame archaic office dress code requirements (the best I can do is Brooks Brothers chino pants and a tucked-in open-collar dress shirt with a belt).
It's an uphill ride to work, so I bought a mountain bike with one of those electric assist motors to help with the sweat thing. It makes riding up a moderate hill no more taxing than riding a regular bike on flat ground.
I thought it would be kinda lame for regular bike purposes, but it actually works out well. The law here says the motor has to cut out at 25kph (16mph). And when that happens, because it is really heavy with the huge battery and motor, it becomes extremely taxing to coax any more speed out of it. But riding around at max speed feels still gets my breathing and pulse up.
So the upshot is that I still get a lot of moderate exercise from the bike, and I can locomote around Tokyo at a pretty much constant 25kph, using either the road or the sidewalk depending on traffic/pedestrian conditions.
And, because I can take a pretty direct route to work, I get there in half the time it takes on the subway.