Bingo and card games such as bridge provide an opportunity for socializing as well as mental stimulation. You have to concentrate at least somewhat to play these. The opportunity to win adds a bit of fun and competition.
Even a person who does not want to socialize can still remain mentally active at home. Most newspapers carry a crossword, and there is a plethora of puzzle books on the market. Research seems to indicate a connection between keeping an active brain and a reduction in some incidences of dementia.
Learning new skills is often associated with youth. But there is no reason why this has to be the case. Learning takes take place at any age. If you are acquiring a new language, playing a new instrument or learning any other skill, you will find mental stimulation. You'll also gain the satisfaction of increasing your knowledge and life skills.
It is easy to slip into a routine, particularly as a person gets older. It can be beneficial to sometimes vary, for example to go to work by a different route. Even a simple change such as working the computer mouse with your other hand can prove an interesting challenge to the brain.