In this paper, we present numerical studies of several different structures of anti-resonant, hollow core optical fibers. The cladding of these fibers is based on the Kagomé lattice concept, with some of the core-surrounding lattice cells removed. This modification, by creating additional, glass-free regions around the core, results in a significant improvement of some important optical fiber parameters, such as confinement loss (CL), bending loss (BL), and dispersion parameter (D). According to the conducted simulations (with fused silica glass being the structure’s material), CL were reduced from ~0.36 dB/m to ~0.16 dB/m (at 760 nm wavelength) in case of the structure with removed cells, and did not exceed the value of 1 dB/m across the 700–850 nm wavelength range. Additionally, proposed structure exhibits a remarkably low value of D—from 1.5 to 2.5 ps/(nm × km) at the 700–800 nm wavelength range, while the BL were estimated to be below 0.25 dB/m for bending radius of ~1.5 cm. CL and D were simulated, additionally, for structures made of acrylic glass polymethylmethacrylate, (PMMA), with similarly good results—DPMMA ∊ [2, 4] ps/(nm × km) and CLPMMA ≈ 0.13 dB/m (down from 0.41 dB/m), for the same spectral regions (700–800 nm bandwidth for D, and 760 nm wavelength for CL).