You have two basic choices: i) use -v to pass the variable to awk or ii) close the ' around the awk script, use the shell variable and continue the ' again.
Use
-vwhile read city do awk -vcity="$city"v city="$city" -F, '{ if ( $1 == "ACTIVE" && $2 == city ){print $1} }' siteDBName >> count done < city_nameClose the quote
while read city do awk -F, '{ if ( $1 == "ACTIVE" && $2 == "'$city'" ){print $1} }' siteDBName >> count done < city_name
I removed the SUM= line since it wasn't doing anything useful given that $1 is ACTIVE so adding it makes no sense. See my alternate approach below for a way to do this correctly.
Also, note that with this approach, you need to read the siteDBName file multiple times. A more efficient version would be:
$ awk -F, '{
if(NR==FNR){cities[$1]++;}
else if($1=="ACTIVE" && $2 in cities ){sum++}
} END{print sum,"active cities"}' city_name siteDBName
3 active cities