First, I think it's really good that you're interested in playing for those audiences--your work will be very much appreciated--they love live performances, and they'll love having talented young people perform for them.
That said--your group is probably too big, and too expensive to get many bookings of the kind you want. You may be able to get $50-75 per person, but it would be for a single or duet--
Anyway, here are a few basic things you should know about:
First--there are both residential and day facilities. In order to be licensed, all the facilities need to provide services that are appropriate to the needs of their participants. This includes recreational and participational activities such as arts and crafts, exercise and music, and, increasingly, life long education.
Day facilities can be "Senior Centers", which can offer drop in activities, gym and pool facilities, counseling and health support, classes, and sometimes meal service. There is also what is called "Adult Day Care" which are supervised day programs for people with physical and cognitive impairments.
Residential facilities include "Independent Living", which can be a hotel-like facility, condos,or cottages with common dining and activities areas(they often promote them as if they are resorts)--in theory, the residents are pretty self-sufficient, and often plan and coordinate the activities, or at least supervise the offerings. One of the places that I worked had a theatre with a full stage, which booked shows in conjunction with the local performing arts center.
Next would be "Assisted Living" which tends to be for people who can no longer live on their own and require some type of ongoing support, but retain some level of mobility. The activities director will provide daily events, often with singing or some sort of musical activity two or three times a week.
The next step would be the "Nursing Home" with a higher degree of support needed--not much mobility, often people are confined to bed and are usually transported in wheelchairs.
There is also "Memory Care" or "Memory Unit" which is for individuals with Alzheimer's, Dementia, and other Cognitive issues. They may or may not be wheelchair-bound, but they have strict supervision. They often have limited ability to communicate.
Each type of facility requires a different sort of engagement--Independent Living would tend to be the most like a regular performance situation, Assisted living might be more of a very interactive sing-along, and Nursing and Memory Care could be much more basic--Memory audiences may not even respond when songs begin or end.
Next has to do with your show. Since you play "jazz", you probably play a lot of standards from what has gotten to be called the "American Songbook"--these are great, because people, especially older people know them.
You may not know this, but people who are 60 and over grew up in times where there was a lot of group singing, there was singing in folk clubs and coffee houses, people sang at parties and in bars, there was a lot of singing on television, and there were even "follow the bouncing ball" sing along shorts in movie theatres. For that reason, in a room with 20 or more people in our age ranges, if you play just about any song along that was popular from about 1920 into the early 60s, people will join in.
The key to being successful is interacting--smile a lot, talk to the audience a lot, interact, let them sing, and get them to respond to you. your musical skills, and even your repertoire run a distant second to your ability to interact.
Recently, I participated in an intergenerational craft and music series that delivered programs in continuing care retirement communities. For my part of the program, I played my ukulele and led the participants thru maybe four or five songs that they requested--as often as not, I worked out the chords as we sang, and I'd go around the room, singing the same words with each table-sometimes we'd get them right, sometimes not, but everyone was having fun, and nothing else mattered. And that is as good as it gets.