Most cruise line cater to the elderly as well as to families. here is some good information and a place where you can find good deals on cruises for seniors; http://www.cruisesonly.com/
I think elderly accommodations on cruises will vary by cruise line. I suggest you contact specific cruise companies to ask them their policies on elderly accommodations on cruises. Before booking any cruises, make sure to double-check that those accommodations are in effect on those particular cruises. Good luck!
There are good and inexpensive two day cruises. You can find good two day cruises on the website www.2daycruise.com/. There are also cruises to nowhere out of New York.
I have heard good things from cruise1st.com for good deals on Alaskan cruises. They are quite highly respected in the knowledgeable community on cruises.
It is possible to find discounted cruises that offer the same extras that the cruise line offers. Some good websites for this are travelocity.com and expedia.com.
European cruises show some of the prettiest places in the world. You can search here: http://www.europecruises.com/ for a list of destinations as well as prices.
Some providers of Pacific cruises are Coastline Cruises, Princess Cruises, and PG Cruises to name a few. These crusies are highly rated and affordable.
There are a number of websites that offer discount and affordable cruises. Some of the good ones are Travelocity.com and Orbitz.com as well as Cruisedeals.com.
Cruises down the Nile are offered by many of the cruise companies. Some examples of good value ones are from the Caribbean Cruise Line and from Princess Cruises.
Some cruises do!
Elderly companions should possess patience, empathy, and good listening skills. It's important for them to be reliable, understanding, and able to provide companionship and support to the elderly individual.
Make sure they have cell phones, a gps, and maps. Make sure emergency numbers are programmed into the phone. Also see if they will pay for AAA service, so they can utilize that if needed.