I travel alone on business extensively. I travel domestically as well as internationally to major European cities such as London, Frankfurt, Paris, Amsterdam, etc. I eat out alone all the time, and will eat at any restaurant that I want to eat at without even thinking about the fact that I will be alone. The restaurants I dine in range from casual spots to Michelin starred fine dining places. I always make a reservation, dress appropriately, and act with utmost appreciation and politeness when arriving at the restaurant. I can say that with very, very rare exceptions, I have been treated extremely well at essentially every restaurant I have visited. I always tip extra well because I am taking a table that would generally be taken by at least two customers. Sometimes I chose to dine at a bar if this seems especially inviting. So...to answer your question, you should dine anywhere in L.A. that appeals to you and not worry about being alone. You will likely be treated very well, and perhaps even better than if you were with friend(s).