One that’s often recommended for older people’s core strength, is getting up from an ordinary chair or sofa, 10 times daily, without using your hands. Keep arms folded in front of you and lean forward slightly.
Another recommended by a physio when I was still a bit weak and wobbly last year after pneumonia, is marching on the spot, but swinging the opposite arm to the leg. Apparently aids balance. At least 50 daily.
You can buy weights online, I have a pair of 1 kg ones which I lift (both up and sideways) while usually sitting on the sofa! (But I don’t do it often enough….)