Since you’re leaving from Houston, TX and heading to Galveston, TX on a Sunday, I’d get going as soon as you can—beach traffic can stack up fast, especially once late morning turns into midday. The drive is straightforward: stay on I-45 South the whole way and expect about 1.25 to 1.75 hours depending on where in Houston you start and how heavy traffic is leaving the city. If you’re aiming for The Bryan Museum first, you’ll want to park on the East End side of town; if you’re not familiar with Galveston, just know parking is a mix of metered street spots and paid lots, and the closer you get to the Strand or Seawall, the more you’ll pay and circle.
Start with The Bryan Museum while the day is still cooler and your energy is high. It’s one of the best indoor stops on the island for Texas history, frontier art, and local context, and it usually takes about 1.5 hours if you’re moving at a comfortable pace. After that, head downtown toward the harbor for Galveston Historic Seaport / Texas Seaport Museum. It’s an easy hop by car—only a few minutes—and it pairs well with the museum because you go from broader Texas history straight into Galveston’s maritime past. If the Elissa is accessible, it’s worth lingering a bit; the whole harbor area gives you that working-port feel that makes Galveston different from a typical beach town. Expect around 1 to 1.5 hours here, plus a little extra if you like reading the exhibits and watching the ships.
From the harbor, wander into The Strand Historic District and just let yourself stroll. This is the part of the day where you don’t need to over-plan: the blocks are walkable, the architecture is part of the attraction, and there are plenty of old storefronts, galleries, and shops to browse without committing to anything big. You can easily spend 1.5 to 2 hours here, especially if you stop for a snack or a cold drink. For lunch, head to Miller’s Seawall Grill on the seawall—classic, unfussy, and exactly the kind of Gulf-front meal that fits a day trip. Figure roughly $20–35 per person, and go in expecting casual service and a good view rather than a fine-dining experience. It’s a smart lunch stop because it breaks up the walking and gets you closer to the beach for the last part of the day.
Finish with Stewart Beach, which is one of the easiest beach stops for a day trip because it’s close to the East End and generally straightforward for parking and access. Give yourself 1.5 to 2 hours here to actually relax—walk the shoreline, sit in the sand, and catch the late light before heading back. If you’re doing sunset, this is the one spot on your itinerary where it’s worth staying put a little longer, but don’t cut it too close if you want an easier drive home. For the return, take I-45 North back to Houston after sunset or before it gets fully dark if you’d rather avoid the worst of the evening flow. The drive is about the same as the way down—roughly 1.25 to 1.75 hours—and if you need gas or coffee, it’s usually simpler to stop once you’re off the island and back on the mainland rather than trying to fight for it in Galveston.