There are a number of budget minded hotels on highway I45 “on” the Island , just over the causeway before 61st street . You are on the island in the morning close to terminals , and on the island the night before close to tourist destinations. I personally do not like Texas City because of all the petrochemical industry and pollution. Galveston is not affected by that issue because of the “prevailing” winds out of southeast , which puts Galveston up wind from the refineries. That is unless there is a wind out of the north from cold fronts , which are short lived .