Not sure if they count as 'suburbs' as they are just half a mile across the Hudson River from Manhattan, but Hoboken, West New York, Guttenberg, Union City, etc in Hudson County, NJ are actually the densest municipalities in America (denser than NYC overall) despite not being within the city limits of NYC proper.
These cities are mostly made up of 4-6 story midrises (brownstones and tenements) built between 1860 and 1930 which might not look as dense as more modern, taller tower blocks. However, they are denser because they don't have parking garages taking up tons of space and are located on narrow streets with no side setbacks or front yards. This sort of "European style" development is outlawed in most of the country nowadays by zoning, especially in suburban jurisdictions, so it's probably not the future of American cities.
Hoboken (40,000 ppl/sq mi):
West New York (49,000 ppl/sq mi):