In three novel peptidoids based on the tryptophan—histidine—tryptophan (WHW) peptide, the central histidine was replaced by Ala-(triazole), and two derivatives also had one tryptophan replaced with pyrene-alkyls of different lengths and flexibility. Pyrene analogues show strong fluorescence at 480–500 nm, attributed to intramolecular exciplex formation with tryptophan. All three peptidoids bind Cu2+ cation in water with strong affinity, with Trp- Ala-(triazole)-Trp binding comparably to the parent WHW, and the pyrene analogues even stronger, demonstrating that replacement of histidine with triazole in peptides does not hamper Cu2+ coordination. The studied peptidoids strongly bind to ds-DNA and ds-RNA, whereby their complexes with Cu2+ exhibit distinctively different interactions in comparison to metal-free analogues, particularly in the stabilization of ds-DNA against thermal denaturation. The pyrene peptidoids efficiently enter living cells with no apparent cytotoxic effect, whereby their red-shifted emission compared to the parent pyrene allows intracellular confocal microscopy imaging, showing accumulation in cytoplasmic organelles. However, irradiation with 350 nm light resulted in evident antiproliferative effect on cells treated with micromolar concentrations of the pyrene analogues, presumably attributed to pyrene-induced production of singlet oxygen and consecutive cellular damage.