Some cities are happy to allow luggage on local transit. Other cities have “premium priced” airport transit that they use to soak tourists, but regular priced transit to serve airport employees. To keep tourists from using the regular price buses, they often impose luggage restrictions.
Honolulu, as has already been mentioned, is notorious for this.
In San Francisco, SamTran Routes 292 and 397 allow luggage, Route KX does not.
In Newark, the NJ Transit local (not express) buses were famous for luggage restrictions, but in checking before I wrote this I notice they now say that two carryon-size pieces are allowed.
You are welcome to bring reasonable size luggage on all the Chicago ‘L’ lines and people do it all the time. Some tips: There are two styles of train cars in use in Chicago. One style has doors that slide into the side of the train and disappear. These cars have four horizontal-facing seats at the side of the doors. If you sit in one of these horizontal seats, you can put a reasonable sized bag upright on the floor in front of your knees without blocking the aisle or taking up an extra seat. Just hold onto them so that they don’t fall over when the train jerks. If you still feel you need to use three seats, sit in the vertical seat (the way most seats face on train) that faces the horizontal seat. Use the half of the horizontal seat nearest you and the floor space in front of it for your luggage.
In both styles of cars, in all but the first and last cars, there will be a folded-up operator’s compartment at one end of the car that has no seat, but does have floor room. In the style of car that does NOT have the sliding doors, at one end of the car is a single seat that was where the conductor used to sir before they eliminated conductors. You can fit luggage behind there, too. Just don’t block the emergency exit at the end of the car.
It’s true that the Quincy station has no elevator, but unless you are incapable of walking down the stairs with your luggage, it will be a far worse hassle to walk an extra four blocks from the Washington station. At the airports, they have nice wide, generously-spaced turnstiles that easily accommodate luggage. But at every station where you might want to get off, they have these narrow turnstiles to pass through. The trick to the narrow turnstiles is to slide your luggage through IN FRONT of you, then go through yourself. Your luggage will fit UNDER
the arm of the turnstile. Also, I don’t know if Quincy has a handicapped gate, but if it does, locate the blue button with the picture of the wheelchair. Press and hold the button for five seconds. Then either push or pull (if one doesn’t work, try the other) the handicapped gate and you can pass through there.