This data is from August 2010. It doesn't specifically answer your question, but I think it does give you an indication. I would think it correct that southern California and the Big Apple have higher density of both IFR and VFR ops than anywhere else.

50 Busiest Radar Approach
Control Facilities
Tracon Ops (000s)
CY
2009 Facilities/State
Rank
1 Southern Calif. TRACON, CA
2 New York TRACON, NY
3 Potomac TRACON, DC
4 Northern Calif. TRACON, CA
5 Atlanta TRACON, GA
6 Chicago TRACON, IL
7 Dallas/Ft Worth, TRACON, TX..
8 Houston TRACON, TX
g Miami International, FL
10 Denver TRACON, CO
11 Honolulu Control Facility, HI
12 Phoenix TRACON, AZ
13 Philadelphia International, PA
14 Charlotte/Douglas Infl, NC
15 Boston TRACON, MA
16 Central Florida TRACON, FL
17 Las Vegas TRACON, NV.
18 Detroit TRACON, Ml
19 Minneapolis TRACON, MN
20 Seattle/Tacoma TRACON, WA...
21 Salt Lake City TRACON, UT.
22 Tampa International, FL
23 San Antonio Infl, TX
24 Jacksonville Infl, FL
25 St Louis TRACON, MO