I don't know why everyone is worried about self defense here.
First of all, highly unlikely you will be mugged in the daytime in the areas we frequent, and usually it's a hit and run, and the mugger is long gone while you're fumbling in your pocket for spray or anything else.
I have been going and living downtown for decades and never got a serious threat, in the daytime. Stay away from brothels on calle 6, lol, or south of Avenida 2, even in the daytime and you should be fine.
Don't get drunk in public.
Don't wear flip flops out in the street. If I see you I might knock you over just for fun and run, even pushing 68 you won't be able to catch me, you tell the world you're an easy tourist target.
COMPLETELY ignore strangers talking to you, don't give any response, keep walking.
Take cabs and Uber at night.
Try to hang with at least one friend, the more the merrier in walking around in public.
Don't go to a ho'z house.
All in all, I lived in S Florida decades and view San Jose as dramatically safer if you use common sense and don't attract attention and don't make stupid decisions.
Of course you can always buy a big long umbrella and go to EPA and get a big steel bar to put in it and bash heads of anyone who looks at you cross eyed, but that would be a last resort...