Polygonum species are used in traditional medicine in many countries; some are also consumed as vegetables in Turkey. The ethanolic, methanolic, and chloroform extracts of four Polygonum species growing in Istanbul, namely P. aviculare, P. patulum subsp. pulchellum, P. lapathifolium, and the only endemic species P. istanbulicum were evaluated for their antioxidant, anti-acetylcholinesterase (AChE), and anticancer potentials. The total phenolic and flavonoid contents of the extracts were determined by Folin-Ciocalteu and aluminium chloride methods, respectively. The antioxidant capacities of the extracts were determined using 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging and ferric-reducing antioxidant power (FRAP) assays. The AChE inhibitory activities of the extracts were determined using the Ellman method. Each extract was screened for cytotoxic activity against NRK-52E and HeLa cervical cancer cell lines using the MTT assay. Among the extracts screened, ethanolic extract of P. istanbulicum showed the highest total phenolic (207.03 ± 14.12 mg GAE/g extract) and total flavonoid (124.95 ± 7.84 mg CE/g extract) contents, and antioxidant activity (DPPH EC50, 8.09 ± 0.50 mg/mL). The chloroform extract of P. lapathifolium exhibited the lowest total phenolic (22.33 ± 3.05 mg GAE/g extract) and total flavonoid (11.66 ± 0.36 mg CE/g extract) contents, and antioxidant activity (DPPH EC50, 218.44 ± 24.46 mg/mL). The extracts exhibited AChE inhibitory activity in a dose-dependent manner, particularly the ethanolic extract of P. istanbulicum which displayed strongest inhibition against AChE (88.2 ± 3.44%). AChE inhibition was minimal (32.19 ± 2.09 to 48.34 ± 3.41%) in the chloroform extracts. All ethanolic extracts revealed cytotoxic activity toward HeLa cells, while they were not cytotoxic toward NRK-52E cells. The ethanolic extract of P. lapathifolium showed the most potent cytotoxicity against HeLa cells (IC50, 8.70 ± 1.35 µg/mL). Results suggested that ethanol was the best solvent for extracting the phenolic, antioxidant, and anti-AChE compounds, and P. istanbulicum may be a potential source of these compounds. Further investigations are nevertheless required to identify the bioactive compounds present in Polygonum species.