The actual construction costs will vary widely depending on where you are (rural or urban) and what you are building (a storage shed or a fine art museum). In the past few years, we have had projects with construction costs ranging from $200 to $800/SF. With the rising cost of steel and the constrained labor market, $200/SF is probably unrealistic anywhere in the country for a building with a controlled environment. One of the benchmarks I often give people is to ask a local real estate or building professional what the construction cost for "A1" office construction is in your city. This is the highest quality office space and is a good starting place for thinking about museum construction costs. Construction costs have also been rising dramatically in the past three years--as much as 20% per year in some markets--so be sure to adjust for that.
When you talk to people, it is critical to distinguish between construction cost and project cost. Construction cost is what the contractor will charge you to build the building. Project cost includes all the other items not included in the construction, such as planning, design and engineering, furniture and fixtures, exhibits, moving, project management, escalation, endowment (sometimes), and contingency. These costs will add anywhere from 50% to 100% to the cost of the project. When you get a square foot cost, be sure to ask what it includes.