Unfortunately, there is not a universal approach regarding to hotel accommodation accessible to wheelers and slow walkers.
Every location differs not only within the United States but also across Europe.
Newer hotels often have better facilities but this cannot be assumed and it is always best to enquire before making a reservation.
Different terminology can mean very different things so it is better to make detailed enquires before deciding if a specific room will suit your requirements. Descriptions can be misleading.
An adapted room may mean that the suite with grand views is fine but reaching it might be almost impossible. Alternately, wheelchair access may get you through the door but not necessarily fulfill use of the bathroom.
Often staff want to help but don’t actually appreciate your specific requirements so try to be patient as they ultimately want to be of service to you.
Don’t be afraid to ask for door measurements or push for a detailed layout of what the room affords. Sometimes floor plans can be faxed or sent on quite easily. You are the customer just like any other able bodied person.
Do not expect reservation travel agencies to be able to provide finite details, politely request to talk to the hotel manager or someone who knows the room that you are enquiring about.
Alternately, explain what you require and let the manager offer something suitable to your needs.
If you set up good lines of communication from the start, it will increase the chance of you being correctly accommodated.