I made a similar trip in late July 2015 after purchasing my 1973 Grumman Traveler (AA-5). The previous owner based the plane near Spokane, WA. Basically flew east from Spokane until almost due North of Dallas, then south to Dallas and direct from Dallas to Sugar Land, TX (S.W. Houston). Flew 1 leg the afternoon of the first day, 2 legs each the next 2 days, and 2 short legs the last day. With the exception of the first day, I tried to finish up each day by mid-afternoon, before the usual afternoon storms appeared.
It was a good trip to become familiar with my new aircraft, and allowed me to build a squawk list to address with my new A&P/IA shortly after arriving home. Only one issue during the trip - the line man at my first stop noticed that the nose gear wheel fairing was crooked. So I had them call out their mechanic the next morning (a Saturday), and after working on it about 2 hours we finally decided to just remove the fairing and put it in the baggage area for the rest of the flight home.
Not a difficult trip, even though my Grumman doesn't have an auto pilot so I hand flew it the entire way. Basically just a series of 2-3 hour long cross countries.
A great way to get to know your new plane and see part of the country, so long as you are already competent flying that plane (I had been flying rented Grumman Tigers AA-5B prior to buying this plane with lots of hours in the type) and you are comfortable with 2+ hour cross country flights.
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