The distribution of fitness effects (DFEs) of new mutations across different environments quantifies the potential for adaptation in a given environment and its cost in others. So far, results regarding the cost of adaptation across environments have been mixed, and most studies have sampled random mutations across different genes. Here, we quantify systematically how costs of adaptation vary along a large stretch of protein sequence by studying the distribution of fitness effects of the same approximately 2,300 amino-acid changing mutations obtained from deep mutational scanning of 119 amino acids in the middle domain of the heat shock protein Hsp90 in five environments. This region is known to be important for client binding, stabilization of the Hsp90 dimer, stabilization of the N-terminal-Middle and Middle-C-terminal interdomains, and regulation of ATPase-chaperone activity. Interestingly, we find that fitness correlates well across diverse stressful environments, with the exception of one environment, diamide. Consistent with this result, we find little cost of adaptation; on average only one in seven beneficial mutations is deleterious in another environment. We identify a hotspot of beneficial mutations in a region of the protein that is located within an allosteric center. The identified protein regions that are enriched in beneficial, deleterious, and costly mutations coincide with residues that are involved in the stabilization of Hsp90 interdomains and stabilization of client-binding interfaces, or residues that are involved in ATPase-chaperone activity of Hsp90. Thus, our study yields information regarding the role and adaptive potential of a protein sequence that complements and extends known structural information.