Another suggestion...I go to Tulsa every January for the Chili Bowl and have been going this way the last 5-6 years to avoid Dallas...
Indian Nation Turnpike south out of Tulsa, to 271 at Hugo to Gadewater, 135 out of Gladewater to Kilgore, then 259 to Nacogdoches, 59 to Livingston, 146 to Liberty, 563 out of Liberty to I-10.
At this point you will have a decision to make. You have avoided all the redlights in Liberty, Dayton and Mt. Belveiu. You can either get back on 146 and go through Baytown, Kemah, Seabrook and have a bunch of redlights and traffic, or take your choice of 2 other routes. Depending on time of day, you could go west on I-10 to loop 610 and south to I-45 and Galveston. Or take I-10 west to Beltway 8 to I-45 southbound. Beltway 8 is a toll road, with no toll booths. I have an electronic pass but I bet they will be happy to mail you a bill. A slightly different way is to go west on US90 from Liberty, catch a few signals in Dayton, then straight into Houston at the intersection of I-10, 90, and 610.
If you get to Houston mid day and dont want the tolls, go the 610 route. You can get to Galveston on 146 but there are countless red lights and traffic through Kemah, Seabrook.
Good luck. I've gone from Liberty to downtown Houston Medical Center 3 times in last 4 days. I need a drank. LOL
Let us know what you do.
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