Not sure why UDC being a HBCU means that it has to be a “lack of options”, unless you mean that most non-black students do not want to attend a college with a high black population.
UDC’s selection of majors may be more of a limitation for many liberal arts students (e.g. no major in economics, philosophy, or physics, for example), though it does have many of the common pre-professional majors (e.g. BArch, accounting, business, civil/electrical/mechanical engineering, computer science, elementary education, social work): https://www.udc.edu/programs/bachelors/
But the VA/MD public universities closest to Washington, DC (GMU and UMCP) are probably too selective to be “broad access” for the purpose of this thread, even if DCTAG may help with the costs (but $10,000 is only about half of the out-of-state extra tuition at GMU and UMCP).