The best place for electric scooters on most city streets is in the regular traffic lanes. This is also the best place for bicycles in most cities. Unless your particular city and route have actually safe bike lanes, you're better off just acting like any other vehicle, using the regular traffic lanes, and following all traffic laws and signs.
(Yes, you're slower than cars; but so is a horse rider, and they've been allowed on city streets since long before cars existed.)
Many sorts of "bike lane" make the streets less safe for cyclists and scooter users. Lanes that are also used as streetside parking are not safe, as attempting to use them requires swerving in and out between parked cars. Narrow lanes that are adjacent to streetside parking are not safe, because of the "door zone" problem. "Lanes" that are really part of the gutter are not safe, because they accumulate debris (tire chunks, mufflers, road sand) -- all of which are much more dangerous for cyclists and scooter users than for drivers.
There do exist high-quality bike lanes in some cities. They are clearly marked and separated from the regular traffic lanes (sometimes with barriers); they don't share space with streetside parking; they often have their own traffic signals.
If there are safe bike lanes, then yes, they're an appropriate choice for electric scooters. The reason for this is that the speed, maneuverability, and vulnerability of electric scooters are much closer to those of bicycles than to either cars or pedestrians.
But if there aren't safe bike lanes on the specific route you need to take, just use the "slowest" (in most of the world, rightmost) regular traffic lane. Most of the time, be in the center of this lane, not hugging the right edge; this makes you more visible, keeps you out of the "door zone", etc. You may move right to allow faster traffic (i.e. cars, trucks, motorcycles) to pass, if it is safe to do so.
(Note: In some places, such as California, cyclists are required to stay to the right insofar as it is safe. This does not mean biking in the gutter or "door zone", because those are never safe.)
Like bicycles, electric scooters should never be ridden on city sidewalks adjacent to buildings. This is because of the risk of colliding with pedestrians coming out of building doors. Blind pedestrians, very elderly pedestrians, pedestrians pushing delivery carts, nearsighted pedestrians who have lost their glasses, and other pedestrians with limited eyesight are all legitimate users of sidewalks. Do not expect that pedestrians can see or dodge. When using pedestrian features such as sidewalks or crosswalks, both cyclists and scooter users should dismount and walk their vehicle.