Personally, if I was unemployed, I'd be looking for a job. But I'd also have an eye to doing a few interesting things with my life ... which I normally don't 'cause I'm working 5 days a week.
So yeah... look for a job with your car... but don't forget to explore the neighborhoods with your bike, check out all the close-by amenities, shops, service that are walkable or bike-able.
And while you're at it, get a couple of interesting books and read them.
Life is too short to be worrying about the next job all the time.