Free Baton Rouge, LA
Baton Rouge is the state capital of Louisiana. Compared to Louisiana's more famous and larger city of New Orleans, Baton Rouge is much more conservative and more in line with other medium sized southern cities like Jackson, MS, Shreveport, LA, or Birmingham, AL. Baton Rouge is the home to TV evangelist Jimmy Swaggart, who in the height of his reign over a vast cult following built a huge 'family worship center' complete with massive apartments for 'religious studies' that still exist off off Blue Bonnet Road. While Swaggart lost most of his empire when he was caught doing drugs with a prostitute in a hotel off Airline Highway in New Orleans, the Family Center still exists - and Baton Rouge remains part of the southern Bible Belt.
The odd name 'Baton Rouge' is actually French for 'red stick'. The French explorers found a pole poked into the ground with animal carcasses spread around it used by the native Americans in the area to mark hunting territory and ward off white settlers. The name stuck.
The weather in Baton Rouge is similar to other cities in the Deep South with mild winters and murderously long, hot, and humid summers. Be sure to drink lots of water and find shade during daytime hours during the deep summer.
Baton Rouge is home to Louisiana State University, one of the largest college in the region. LSU is huge and even provides completely free bus system in the neighborhoods surrounding it and to and from the Florida avenue city bus terminal. Also located in the northern part of the city is a major majority-black university, Southern University.
If you avoid some of the higher rent areas, cheap apartments can be found.
Tigerville near LSU is a vast section in South Baton Rouge that has very inexpensive housing. Efficiencies (as of 2010) can be found for as low as 275 USD to 350 USD a month. However, the landlords in this area tend to be VERY picky and have a habit of discriminating against anyone who is not a Louisiana State University College student. Expect to have to go to the cops to get a criminal background check out of your own pocket, have paycheck stubs showing you make triple the rent, and pay application fees with no guarantee of getting in.
Gardere has inexpensive apartments, but is plagued with high crime.
Off of Sherwood Forest Drive in North East Baton Rouge, there is one no-deposit, utilities paid apartment called "The Brandywine" for 450 USD a month. However, it is in a bad area and actually suffered full scale riots in 2009 when the power workers cut the power to the complex for a month and the landlord still charged rent!
In the Mid-City area, there are rooms for rent that range from 75 USD to 100 USD a week. The neighborhoods vary.
If a weekly rent motel is needed, looking on Airline Highway will be more reasonable, but expect to pay 200 USD a week to 230 USD.
THE SALVATION ARMY TRANSIENT LODGE - BR (225) 355 4483 2.14 miles from city center Baton Rouge 7361 AIRLINE HIGHWAY BATON ROUGE, LA
There are others, but they tend to be scattered in the parish.
There is a food pantry open on certain days for those who may find themselves short on food. It all tends to be mostly canned stuff, but varies by week:
Greater Baton Rouge Food Bank Greater Baton Rouge Food Bank 5546 Choctaw Dr Baton Rouge, LA 70805-7117 (225) 359-9940
LSU's Charity Hospital is being rebuilt in New Orleans... despite local parish politicians (and LSU's administrators who are tired of commuting to New Orleans) best efforts to move Charity to Baton Rouge.
There are free clinics that LSU operates out of Baton Rouge General (both locations), but usually require a letter from a social worker or some sort of government agency.
The nearest ACLU chapter is in New Orleans.
ACLU of Louisiana P.O. Box 56157 New Orleans, LA 70156 (504) 522-0617
If you or a buddy has weed bust problems, NORML has no office here, but you can always check their website. 
Alcohol can be bought any time except 2 am to 4am on weekdays and 2am to 11 am on Sundays (when the locals want you to be in church). If you are hell bent on getting a beer during no-serve times, you will have to cross the Mississippi River bridge to Port Allen, LA in West Baton Rouge Parish where booze is served 24/7. Like most towns in Louisiana, hard liquor can even be purchased in liquor aisles of convenience stores and grocery stores. However, this IS NOT New Orleans or even the parishes surrounding New Orleans and you WILL be messed with by the East Baton Rouge Parish Cops if you are caught walking around with your beer or otherwise acting a fool.
If you are caught with pot - and that is even considered residue out of a pipe! - the Baton Rouge cops will haul you into jail for a week or more! For all the liberal policies with drinking, Louisiana is one of the most oppressive states when it comes to drug laws.
Baton Rouge, like all cities in Louisiana, does have a watered down version of Mardi Gras.
Perkins Rowe is Baton Rouge's 'CorpGov family-friendly' version of New Orleans' French Quarter. It has some very expensive restaurants, a nice cinema, a whole foods place for rich bohemian wannabes, and a book store. Of course, no public drinking like New Orleans.
The LA state capitol building is located downtown and is a giant building jutting out to contract Baton Rouge's otherwise flat landscape and can be seen for miles. It is also the building pictured on the state quarter.
In downtown Baton Rouge, there is a paved river walk where you can watch the traffic on the mighty Mississippi River. It can be a quite peaceful, meditative experience when the weather is nice.
If you like your liquor on the sickening sugary side, all of Lousiana is known for daiquiris. A daiquiri is like an alcoholic slushy. Some of these even have a drive through and are located throughout the city.
Baton Rouge has numerous festivals and parades, but unlike New Orleans (which closes down wide swaths of the city with each party) tends to keep it subdued, short, and in one area. Check the papers for events.
There are no underground papers. The CorpGov approved major paper is called The Advocate.
NOTE: While Baton Rouge does have some public transit, it is strongly recommended that you get a bike as well. Working class drones have been known to have to get up at the crack of dawn and take 2 buses waiting 45 minutes plus between each just to get to work and taxis are very slow and very expensive. At least, unlike Jackson, MS or Birmingham, AL there are definite bike ride-able areas that are not highway where you could get run over by an SUV.
Baton Rouge has a public bus system called CATS, but is known by locals to be sometime unreliable with funny schedules and transfers that may leave you waiting at another terminal for an hour for a bus, if you are not on one of the two or three major arteries. The bus starts running at 6 AM and stops about 8 PM. The bus does carry bike racks, so you can use the bus in tandem with a bike. The main bus station is at the Florida Street Terminal near downtown Baton Rouge. The fare is $1.50 and 25 cents for a transfer (2011). If this was not bad enough, the middle class and upper class denizens of Baton Rouge have been pushing lately (2011) to cut funding for the public bus even more because they all have gas guzzlers and do not want to pay more property taxes so the working class that cooks their meals and cleans stuff can get around! The locals are in the process of a massive "Save Our Bus System" campaign that probably is not going to work since Baton Rouge has a long history of old money built on slavery and racism.
The Tigerville/LSU area has TigerTransit bus system which is free to everyone. But, it only goes around the neighborhoods surrounding LSU and to LSU itself and to the CATS Florida Street terminal. 
If you need to get to New Orleans on the cheap, the LA Swift will get you there for 5 USD. It runs from about 6 AM to about 7 PM and leaves around every 2 hours. It leaves from the same Florida Terminal that CATS is based from and drops you off at Elk Place at Canal Street in New Orleans. Some trips will also make quick stops in some of the smaller towns between New Orleans and Baton Rouge like Gonzalez, Sorrento, and LaPlace. 
The Greyhound bus terminal is located on Florida Blvd several blocks east of the downtown public bus and LASwift terminal. From here, with enough cash, you can exit the city to anywhere you want. Immediate destinations include New Orleans, Jackson, Shreveport, Lafayette, and beyond.
The public airport is located in the northern part of the city. It is served by the public bus system.
Free Clothing and Furniture
There is a very well stocked Goodwill on College Drive. Google will list other locations, but this is the only one still open. It is not 'free', but the prices are very cheap.
Goodwill's website 3121 College Dr # B, Baton Rouge - (225) 926-1868