Structural properties of a small hexapeptide molecule modeled after metal-binding siderochrome immersed in a room-temperature ionic liquid (RTIL) are studied via molecular dynamics simulations. We consider two different RTILs, each of which is made up of the same cationic species, 1-butyl-3-methylimidazolium ($BMI^+$), but different anions, hexafluorophosphate ($PF_6{^-}$) and chloride ($Cl^-$). We investigate how anionic properties such as hydrophobicity/hydrophilicity or hydrogen bonding capability affect the stabilization of the peptide in RTILs. To examine the effect of peptide-RTIL electrostatic interactions on solvation, we also consider a hypothetical solvent $BMI^0Cl^0$, a non-ionic counter-part of $BMI^+Cl^-$. For reference, we investigate solvation structures in common polar solvents, water and dimethylsulfoxide (DMSO). Comparison of $BMI^+Cl^-$ and $BMI^0Cl^0$ shows that electrostatic interactions of the peptide and RTIL play a significant role in the conformational fluctuation of the peptide. For example, strong electrostatic interactions between the two favor an extended conformation of the peptide by reducing its structural fluctuations. The hydrophobicity/hydrophilicity of RTIL anions also exerts a notable influence; specifically, structural fluctuations of the peptide become reduced in more hydrophilic $BMI^+Cl^-$, compared with those in more hydrophobic $BMI^+PF_6{^-}$. This is ascribed to the good hydrogen-bond accepting power of chloride anions, which enables them to bind strongly to hydroxyl groups of the peptide and to stabilize its structure. Transport properties of the peptide are examined briefly. Translations of the peptide significantly slow down in highly viscous RTILs.