Here are a few pre-recommendations:
You don't need to say which airport you'll arrive at (Houston and Austin are only a couple of hours apart, which is a blink of an eye in Texan terms), but it'll help with specific suggestions.
You do need to say here what you said in your other query--that you're looking for a Harley or Triumph, if that's truly important.
You definitely need to say how long a time you want to spend riding in the US, since suggestions will be very different for a five day trip vs. a monthlong journey.
It'll really be helpful if you state what sort of riding you want to do. Your interest in Harley Davidsons suggests big, open-road journeys of the sort which bore me to tears, so if that's the case I'm going to leave suggestions to others, but without some clarity from you I'm just guessing wildly.
And you need to say what you like to actually do and see: cities, countryside, mainstream or alternative culture, mountains, deserts, music, arts, festivals,
joints and roadhouses, trashy roadside attractions, camping or hotels, etc. etc. etc.
Any clarification by you will increase the chances that responses will be useful, in addition to making it more appealing to go to the trouble of responding. Hope that's helpful.
Mark