I am getting an angiogram, but the hospital can't perform an angioplasty, if needed. Is it better to change to a hospital where they do both?

Yes. If there is a blockage is found during angiogram, it can often be treated during the same procedure, with angioplasty and/or stent placement. This can eliminate the necessity of a second procedure. There are risks associated with the procedure which you should understand prior to proceeding.