If your new man doesn't want to give you his phone number or refuses to answer your calls and only respond via text message, it could be that there is someone on his end who he doesn't want to hear him talking to you. Take into account factors such as whether he's at work or out with his friends, but if happens continuously and you still feel uneasy, ask yourself who is it he doesn't want to overhear your conversations.
People in new relationships usually want to show off their new-found love. If he seems reluctant to introduce to you to his mates and family, or if he takes you on dates to new places where he doesn't know anyone, chances are he's trying to keep you hidden. Is he embarrassed to be seen with you, or is he worried who might see him? Ask him on dates on special occasions such as Valentine's Day and Thanksgiving. If he makes excuses, it may be he's celebrating with somebody else.
If your new man always arranges to see you at strange times, ask yourself why. If he always turns up immediately after work, he could be using the "working late" excuse with his partner. If he always turns up in sports gear, maybe he is pretending to be at the gym. Ask him to come for dinner, and specify he should wear his best clothes. If he is reluctant or wants to get changed at your house upon arrival, this should definitely set alarm bells ringing.
If you find yourself always meeting your new man in bars, hotels or your place, suggest he cook for you at his house. If he suggests a nice meal at a restaurant instead, this could make you wonder why he doesn't want you at his place. Even if he shares his house with other people or parents, there should be no reason why you can't visit, even if it's just to watch a movie. If he doesn't even want to tell you his address, there is a good possibility he does not want to risk you turning up on the doorstep.