I would say yes it is.
Strength training improves metabolic health, muscle mass and effectiveness (no, you won't bulk up, you'd have to massively and intensively work at it to do that), and importantly for women, bone density to counter osteoporosis.
There are four main components it's important to train: cardio, (which you sound like you already have from running), strength, balance and flexibility.
Balance naturally declines with age and training it reduces the risk of having a fall. Likewise flexibility means you're more able to recover from being off balance, and less likely to injure yourself by making a movement beyond your natural muscle or joint range.
You don't have to strength train in a gym though. Rock climbing (indoor or outdoor), kettle bells or dumbbells at home, tough mudder/obstacle type races where you're lifting your bodyweight (playgrounds or outdoor adult gyms ditto), push ups, getting a pull up bar, there are plenty of other options than the gym.
You also might find you enjoy it more than you think if you try it though.