Don't know if you're talking about both lunch and dinner. But when I've had lunch at Providence,
there seem to be a numer of regulars dining alone at tables. BTW...they only serve lunch on Fridays. And I agree with the early comment....I would go anywhere alone that I would go to with friends.
Very nice solo dining and great food at the bar counters at:
Osteria Mozza (right in front of the mozzarella bar)
6602 Melrose Avenue, Los Angeles, CA 90038
2709 Main Street, Santa Monica, CA 90405
435 N Fairfax Ave, Los Angeles, CA 90036
6602 Melrose Ave, Los Angeles, CA 90036