You will be 100000% fine and happy living in Cambridge. My husband doesn't drive at all and we don't own a car; we've lived here for 10 years and about 7 jobs between us and have been just fine. You can do everything you listed and more without a car.

That said! It's nice that your household has a car, because you can explore a little more without being limited to transit, it's nice to get outside of the city sometimes, and it's helpful for grocery runs etc. I rent a car occasionally for errands, to visit friends who live in the 'burbs, etc.

If you look for in-person work your job search will be slightly limited by needing to be accessible to you by transit in a reasonable amount of time... but doesn't everybody limit their job search based on commute? To me that isn't that big a deal.