71.89 miles to Franklin, Washington
AS an aside, I grew up on a Franklin STREET, in Ohio
I only checked against the Essex County Franklin, I didn’t realize there’s more than one. But as it turns out, I live 2.57 miles from the Franklin in Morris County. 
I live around 25 miles from the northern boundary of Franklin County, PA. The county line runs along Morris Street in Shippensburg.
Robin
After opening this can of worms, which I did mostly “for the fun of it,” I have begun to suspect that I have yet to locate anything definitive on just how many legitimate Franklins are in the USA. Not counting the additional confusion as it relates to counties and townships, the listing in Wikipedia, sorted and alphabatized, seems to be at odds with the Census Bureau link in the OP.
I have set myself the task of organizing the posted remarks into this structure and trying to account for any towns, cities, villages, etc., not already on this skeleton list. I’m not promising any quick conclusion to that effort, but those of you who have read and not posted yet, here’s something you can use as a guideline.
Please feel free to add to and/or correct the entries.
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In American geography:
Franklin, Alabama, town in Macon County, Alabama, United States
Franklin, Arkansas, town in Izard County, Arkansas, United States
Franklin, Connecticut, town in New London County, Connecticut, United States
Franklin, Georgia, city in Heard County, Georgia, United States
Franklin, Idaho, city in Franklin County, Idaho
Franklin, Illinois, village in Morgan County, Illinois, United States
Franklin, Indiana, city in Johnson County, Indiana, United States
Franklin, Iowa, city in Lee County, Iowa, United States
Franklin, Kentucky, city in Simpson County, Kentucky, United States
Franklin, Louisiana, the parish seat of St. Mary Parish
Franklin, Maine, town in Hancock County, Maine, United States
Franklin, Massachusetts, city in Norfolk County, Massachusetts, United States
Franklin, Michigan, village in Oakland County, Michigan, United States
Franklin, Minnesota, city in Renville County, Minnesota, United States
Franklin, Missouri, city in Howard County, Missouri, United States
Franklin, Nebraska, city in Franklin County, Nebraska, United States
Franklin, New Hampshire, city in Merrimack County, New Hampshire, USA
Franklin, New Jersey, Borough in Sussex County, New Jersey, United States
Franklin (town), New York, town in Delaware County, New York, United States
Franklin (village), New York, village in Delaware County of the U.S. state of New York
Franklin, Franklin County, New York, town located in southeast Franklin County, New York, USA
Franklin, North Carolina, incorporated town located in Franklin Township
Franklin, Ohio, city in Warren County, Ohio, United States
Franklin, Cambria County, Pennsylvania, borough in Cambria County, Pennsylvania, United States
Franklin, Venango County, Pennsylvania, city in Venango County, Pennsylvania, United States
Franklin, Tennessee, city in Williamson County, Tennessee, USA
Franklin, Texas, city in Robertson County, Texas, United States
Franklin, Vermont, town in Franklin County, Vermont, United States
Franklin, Virginia, independent city in Virginia
Franklin, West Virginia, town in Pendleton County, West Virginia, United States
Franklin, Jackson County, Wisconsin, town in Jackson County, Wisconsin, United States
Franklin, Kewaunee County, Wisconsin, town in Kewaunee County, Wisconsin, United States
Franklin, Manitowoc County, Wisconsin, town in Manitowoc County, Wisconsin, United States
Franklin, Milwaukee County, Wisconsin, city in Milwaukee County, Wisconsin, United States
Franklin, Sauk County, Wisconsin, town in Sauk County, Wisconsin, United States
Franklin, Vernon County, Wisconsin, town in Vernon County, Wisconsin, United States
52.7 miles and I didn’t even know there was a Franklin in Connecticut. I Googled jsut on a whim.
Wow.
220 miles to Franklin NY and 102 miles to Franklin, MA.
There, now you can triangulate me.
According to Mapquest (and Juggernaut upthread), there are four Franklins in New Jersey–Hunterdon, Essex, Morris, and Sussex counties. As well as Franklin Lakes, Franklinville, Franklin Grove, Franklin Corner, and Franklin Park.
I dare you to prove it. I don’t believe that there is a Franklin in Florida, which should put us both pretty far away from the nearest Franklin.
According to Wikipedia there is a Franklin Park*, in Broward, and a Franklin County (up near Baja Alabama). Alas we do have a tiny Springfield as well. I was kind of hoping we had neither. And I’m still not counting “Franklin Park” as “Franklin”. I would have accepted “Franklin City”, “Franklintown”, “Franklinville” or “Franklinburg”.
*Population less than any public school I’ve ever attended
For me, riding my bike to downtown Franklin, having an ice cream cone at Ben & Jerry’s, and riding back is a good day’s outing. It’s probably about twenty miles each way.
I live in New York, but all of the NJ Franklins are closer than the one in New York. The closest is 54.5 miles away, according to Mapquest.
I’m guessing you do Roonwit. I lived 19 miles from the big F growing up. I grew up in LaGrange.
The Franklin in Essex is also the one that I used. By the way, in case you have any internet stalkers, you probably shouldn’t give your distance from any of the other Franklins. 
Hmmmmm…
I will have to check after work but, as I recall, Franklin IN starts at the Christina House on 31 (at least per the post office and school districts) and I believe my house in Whiteland is about 1.7 miles north of that. My wife put in an application to be a CNA there and I think that is how far it is but I will need to double check. She did work as a CNA at the Masonic Home though.
Not that this counts for anything, but I was borned in Franklin IN, Johnson County Memorial.
Probably should have looked it up before I posted, but, the driving directions from Yahoo Maps put me at 1.5 miles north of Christina Blvd.
Does this mean I’m winning?
I still can’t believe no one here actually lives “in” a Franklin.
Sorry, Christian Blvd, where the Christina House is, the northern edge of Franklin IN.
Franklin Park is a subset of Franklin Township, Somerset County.
Bah, I know nothing about anything south of Morristown. 
825 miles from Franklin, AZ
764 miles from Franklin, SD
663 miles from Franklin, KS
405 miles from Franklin, NE
There don’t seem to be any Franklins in Utah, Wyoming, Colorado, or New Mexico. But I still don’t beat lightningtool
And I was so close. Yahoo says 4 miles from my driveway to (about College and Pennsylvania) to the corner of 27th and College.
Ahem. I do. I posted that almost exactly 24 hours ago.
If there’s a prize, I win.