The Tremont is just...nice. Fully restored and resembles upscale hotels in downtown venues. It is a block from The Strand, a nice corridor of stores and restaurants, that allow for the tourist in you to come out. I stayed only one day, but was impressed with the room. I, too, stayed in 246 and loved the high ceilings, hardwood floors and contemporary feel. My only complaint was lack of electrical outlets. There is a desk in the room, free internet, but no place to plug in!!
Galveston has recovered quite remarkably. The Old Town area is amazingly alive, with lots of shops and restaurants, some along the bay. The Tremont offers a really nice respite to explore this area, as well as take in the beach. Highly recommended.