We discuss the feasibility of different kinds of curved space-times as backgrounds for string theory. This thesis is divided into two parts. First, we focus on the double copy procedure and apply it to the Born-Infeld solution in open string theory in the approximation when field-strength derivative terms can be ignored. This process leads us to a generalised version of the Schwarzschild metric which looks non-singular at the origin. Whether this metric is a solution to some closed string equations of motion is also discussed. In the second half of the thesis, Kundt space-times are studied. We show how it is possible to obtain solutions to the Weyl anomaly equations for a background formed by a Kundt metric and a dilaton. The inclusion of a B-field is mentioned but not implemented.