Panhandleborn

I agree that the Sunflower Cafe is the place to go for breakfast. We haven't found any place that beats it so far. When we are in Galveston it is our go to place for breakfast. 

We like the Tremont which is on the Strand.  Close to great restaurants, shops, and every thing. We also like Hotel Galvez on the seawall. Close to many restaurants and across from the water. We like Moody Gardens if we don't plan on doing much since it is a drive to anything. If looking for a B&B; the 1890 Freeman house or the Mansion on 17th are great.  About 2 blocks from the Strand and 3 blocks to some great restaurants that the locals go to. 

Sunflower Cafe is fantastic. It is our go to breakfast place when we are in Galveston. 

We like a B&B called Schaefer Haus.  It is nice, quiet,  close to the Strand, and on the start of the historic at East end. I don't know about transport to the pier.