100% agreed that you need to find places you have a genuine interest working for. Find somewhere that resonates with your personal values, goals, ambitions. A famous public figurehead who you admire, or something important that the company has done that you want to be a part of. Make a list of places like this that are really important to you.
Then write sincere, dedicated cover letters and mail them along with your resume. Show them a passion, enthusiasm, and most of all, what you could offer them and why it is important that they consider you for a position. The best cover letters are the ones that show exactly why you care, and make them care about you at the same time.
It certainly won’t hurt your chances of getting hired, and it’ll probably feel good too.