The Segway is - by definition - a two wheeled device.
There are many, probably hundreds, of different kinds of scooters, carts, chairs, and other "mobility assist devices" on the market. Some are quite good and some are, at best, "somebodies half-developed wild idea."
The "bottom end" of mobility devices suitable for those who need/want one are the light weight scooters. Some come apart for easier transport and are called "travel scooters." For the come-aparts, the largest single part generally is around 35 pounds, and 3 or 4 "units" when disassembled are about typical.
Scooters have three or four wheels, (plus a couple of anti-tip castors) and generally have small (~ 10 Amp, 30 volt) motors. Prices for the lighter weight ones, if your insurance is paying, generally start at about $1,200 (US), but "retail" versions can be found for about $900 from Walgreens, Walmart, Sams, etc (generally only via web order).
The "retail bargain" scooters generally have no useful support if something goes wrong, and are suitable only for use indoors, or in good weather on dry level hard-paved surfaces. Most of the light weights are "rated" for maximum passenger loads of 150 lb or less. Most of the light ones have at most about 4 inch diameter wheels, and a fat garden hose, a gravel parking lot, or grass more than about 3 inches tall may be an impossible barrier for the smaller ones.
Most of the travel scooters and other lightweight ones quote about 10 or 12 miles range on a single charge, which usually is sufficient for the places where their use is appropriate - for one day at a time.
Heavier scooters, with drive wheels 6 inches or larger usually have a more robust motor and larger batteries. Motors generally are in the 30 Amp, 30 Volt range. Some of these can climb a 3 inch (or even a little higher) curb and can get through the gravel and grass much more easily. Load ratings generally start at about 200 lb, and higher capacities are available. (Even if the passenger is only 100 lb, one who carries a banjo and a six-pack may need a higher capacity transporter.)
Motorized chairs, with two larger drive wheels and anti-tip/stabilizer wheels front and back generally are in the weight/power range with the heavy scooters.
The larger scooters and motorized chairs probably start at around $2,000 list prices, and go up for a long way.
Both the heavier scooters and the motorized chairs are heavy and powerful enough to be dangerous both to the occupant and to persons, objects, and structures in the near vicinity if not operated safely and carefully. Most "care facilities" where one has been used have the holes in the walls to show the hazards. They don't like to talk about the "injured others."
Operating range on a single charge for these heavier units is usually advertised as something like 25 miles "on level paved surfaces." This may be sufficient for more than a single day of use between recharges, in some places and for some users. Battery condition (affected by both aging and charging practices) may significantly affect the useful range. These larger units are heavy and generally require ramps or heavy duty hoists for loading and unloading for transporting.
I have not found any of the above kinds that is "weather tolerant." If you drive any of them into a puddle of water more than a half inch deep you may have to replace the entire (lower) control unit - at about half the price of a new transporter.
Fairly small two-person carts exist, but I've only seen a few from a distance, and haven't found much specific/useful info on the web for any of the ones I've seen. No local dealers in my area handle them so far as I know.
Larger "carts" and "street scooters" are available, with some having full "street legal" lighting and other accessories, with ranges of 30 to 50 miles or more and top speeds up to 30 mph (or more); but they are rather expensive and probably not suited to the uses of interest here.
In some communities, golf carts are "street legal" with minimal modifications; but that's not generally the case where I've had experience. These are both difficult to tranport between places where they are useful, and usually require more maintenance (effort - and sometimes cost) than the "medically intended" vehicles.
(The unit linked by heric is not street-legal in any place of which I'm aware, and should not be operated on the street. I've looked at many similar ones, and they should be used only for "recreational" purposes.)