The goal of this paper is to introduce integer location problems. These are continuous location problems in which we look for a new facility with integer coordinates. We motivate why research on integer location problems is useful and sketch an application within robust optimization. We then analyze the structure of optimal integer locations: We identify integer location problems for which a finite dominating set can be constructed and we identify cases in which the integer problem can be solved by rounding the solution of the corresponding continuous location problem. We finally propose a geometric branch-and-bound procedure for solving integer location problems.