* Celebrations after president announces will stand down
* Some media restrictions lifted immediately
By Tarek Amara
TUNIS, Jan 13 (Reuters) - Tunisians emerged from their homes into what seemed a different country after watching their president set a date for leaving office on Thursday.
Zine al-Abidine Ben Ali, who has led Tunisia for more than 23 years, bowed to pressure from weeks of unrest and announced on television he would step down in 2014, ordered police to stop shooting protesters and promised a free media.
Tunisians, who have chafed at the restrictions on civil freedoms imposed by his administration, waved flags, danced, honked car horns and sang the national anthem.
"We did not expect this speech," said one man, Mohamed Ali, in the Lafayette area of the capital where hours earlier police shot at protesters. "The most important thing is liberty, liberty, liberty."
Sonia Ayari, another person celebrating in the street, said: "We salute Ben Ali's courage, even if it came late."
In the El Omran neighbourhood on the outskirts of Tunis, women poured into the street, ignoring a curfew imposed the day before, and shouted "Viva Ben Ali!"
Even in the towns in Tunisia's less-prosperous interior where dozens of people were shot dead in clashes with police, many people -- though not all -- were jubilant.
"After a day of violence everything has changed. There is only joy here now," trade union activist Ismail Smida said from Tataouine, 500 km (310 miles) south of Tunis. "About 4,000 people have come out to say thank you to the head of state."
In Sidi Bouzid, the town where the wave of unrest started when a jobless man set fire to himself in December in an act of protest, a few people sang and danced in celebration, according to union activists there.
State television, normally a staid affair devoid of any criticism of the authorities, was suddenly transformed.
Figures like Ben Ali opponent Taoufik Ayachi and the ousted head of the journalists' union Naji Baghouri -- all previously kept off the airwaves for their anti-government views -- appeared on an evening broadcast.
Viewers could see a lively debate about Tunisia's media during which one guest broke a taboo by criticising a member of the president's family.
The change was also felt in cyberspace. Blocked Internet sites YouTube and Dailymotion started working again soon after Ben Ali's speech. The Internet site of French newspaper Le Monde was accessible for the first time in months.
The Tunisian government had been trying to hinder opponents using the Internet, especially social networking sites, to organise and circulate information, prompting criticism this month from the U.S. State Department.
"We have seized our liberty after 23 years," said one person posting online updates under the name Ayman. "Finally, freedom." (Writing by Christian Lowe; Editing by Jon Hemming)