Las Vegas is the number one destination for senior citizens in the USA. There are a lot of entertainment opportunities plus non-stop gambling in Las Vegas, and that combination seems to attract many older folks. Most people visit Las Vegas for one week, and they spend a lot of that time in the Casinos. How long you stay depends on your interests.
There are plenty of entertainment venues including the extravagent, and expensive, Las Vegas variety shows. There are also Broadway style musicals, famous name entertainers, and numerous musical groups. If you have enough money, you could easily see a major show every night of the week, and see a well-known singer, dancer or musician four or five times a week. You could hear at least five different musical groups every day without repeating the same act.
There are hundreds of eating choices including the famous all-you-can-eat buffets, the signature restaurants of the famous chefs from around the world and every type of cuisine immaginable. The weather in September will be very warm if not downright hot. You can lounge around the swimming pools with their artificially cooled waters and work on your suntans. You can take a tour bus or helicopter tour to the Grand Canyon, Boulder Dam or the Valley of Fire. I don't think you will find any shortage of diversions to keep you occupied in Las Vegas.
San Francisco is a beautiful city on hills overlooking a photogenic blue bay. Phoenix is a sprawling, rather congested desert city just like Las Vegas but without all of the attractions. It is a nice place to play golf or relax around a swimming pool, but it does not offer any great scenic attractions.
I suggest you take a shuttle to Los Angeles just four hours by car or one hour by airplane. It is also a large congested city, but at least it offers many nice beaches and some tourist attractions like Hollywood, Disneyland and Beverly Hills. If you prefer less congestion with nice beaches, you can go to San Diego just two hours further south. From Los Angeles or San Diego, you can rent a van and drive the coastal highway north through Santa Barbara, Big Sur and Monterey to San Francisco. It is a beautiful drive that can be done in a single day, or two days with time to enjoy the sights. Then, spend a few days appreciating the beauty and the fine foods in San Francisco.