Should I, or shouldn't I?!?

I'm wanting to go on a much needed vacation, and I was thinking Corpus Christi, Tx. The problem is, I'm a first time flier, and traveler, AND I'm going by myself. Do you think this is a good idea? Everyone I have told has said it's a bad idea cause I'd be alone. I think it would be good for me to go and get away. I think I could handle myself anyway. Opinions please!! ♥ THANKS!