I had to leave my first RN position after 6 months a year ago do to relocating, and didnt have any problem finding a job in Houston. They didnt like my little experience, but they said they lied my personality and enthusiasm-- so really sell it during your interviews!! For example, the job I have now required 2 years experience and an BSN because it is in the medical center, and I got it with only 6 months exp and an Associate Degree...
You can also try North Cypress Medical Center off 290/huffmeister..it is a little further, but it is another option if the others dont hire you. Also, if you have a heartbeat, Triumph will hire you-- it is a LTAC but starting pay for new grads is $30 an hour DAYS with 6 : 1 nurse patient ratio. I turned it down because I love the specialty I am in and wanted to hold out a little longer for the perfect fit.
I turned down 2 other jobs , one at North Cypress medical Center and another at an HCA hospital. Totally stupid of me looking back, but I ended up getting my dream job, so it all worked out!!!
Hang in there! You will find something in Houston, just don't give up !!! I didn't :)