I live near Washington, DC and - I've not done it - but I'd think visiting the Smithsonian museums downtown would be quite doable. They are all free as well so that's a money saver (a few are affiliated with other groups and do charge - like the Newseum or Spy Museum, etc). I'd also think you could scooter around The Mall (the giant green space with the monuments - most museums surround this space). There's a lot of open space. Although I rent a scooter at WDW I don't when I go downtown - mostly cause it would be inconvenient to rent one for a few hours. Since I live here I usually just go down to see one thing and know how to get there and back with the least amount of walking - haha! (or if my knees are really bothering me I just go another time). Even if it means uber, etc., I manage it that way. DC reminds me more of WDW in terms of a relatively confined area with a lot of wide open space and being able to scooter from a hotel is a plus. I think our metro system is friendly to mobility devices but always make sure the stop where you're headed has a working elevator (they sometimes go out of service for repair).
There's also a great bus I use called the Circulator which has an amazing downtown loop and is $1 a ride at most. If you can walk some but not the long distances - this can work great. They also have accessible busses:
https://www.dccirculator.com
I've been to NYC a few times since my knees have gotten terrible. I cannot imagine trying to use an ECV there downtown or a WC - just cause of the crowds. I usually book at hotel where I want to be (Times Square are which is bloody expensive) and use a taxi/uber for anything else. However in comparison I'd think Washington, DC would be much easier to navigate. You could also find hotels within scootering distance of the National Mall.
https://washington.org/dc-information/washington-dc-disability-information
https://wheelchairtravel.org/washington-dc/monuments/
I don't know anything about this site but it looks interesting:
https://wheelchairtravel.org