Emerging and re-emerging viruses periodically cause outbreaks and epidemics around the world, which ultimately lead to global events such as the COVID-19 pandemic. Thus, the urgent need for new antiviral drugs is obvious. Over more than a century of antiviral development, nucleoside analogs have proven to be promising agents against diversified DNA and RNA viruses. Here, we present the synthesis and evaluation of the antiviral activity of nucleoside analogs and their deglycosylated derivatives based on a hydroxybenzo[4,5]imidazo[1,2-c]pyrimidin-1(2H)-one scaffold. The antiviral activity was evaluated against a panel of structurally and phylogenetically diverse RNA and DNA viruses. The leader compound showed micromolar activity against representatives of the family , including SARS-CoV-2, as well as against respiratory syncytial virus in a submicromolar range without noticeable toxicity for the host cells. Surprisingly, methylation of the aromatic hydroxyl group of the leader compound resulted in micromolar activity against the varicella-zoster virus without any significant impact on cell viability. The leader compound was shown to be a weak inhibitor of the SARS-CoV-2 RNA-dependent RNA polymerase. It also inhibited biocondensate formation important for SARS-CoV-2 replication. The active compounds may be considered as a good starting point for further structure optimization and mechanistic and preclinical studies.