The 2002 Census of Governments reports that there were 87,525 local governments in the U.S., of which almost 36,000 were cities or townships. I have never seen a survey that determines how many people know what city they reside in. Postal city addresses often do not match municipalities.
We do know something about voter turnout. It tends to be small for local elections. Table 419 of the Statistical Abstract of the U.S. (2003) shows percent voting in even-year elections only. In the 1998 Congressional elections, 41.9% of the voting age population voted; as expected, it was slightly higher in 2000 (the last year reported in this Table) with 54.7% of eligible voters voting.
Data on off-year local elections are harder to come by. We calculated that for just California, in 2001 only 15% of eligible voters went to the polls (114 local elections); in 2003 it was 24% (96 local elections).
Researchers still estimate rank-size relationships from city population data. Why? These are seldom economic units, being defined by arbitrary boundaries. And the voting statistics suggest that cities also lack political significance for most people.