Gintama is set in a period of relative peace after Edo was invaded by the Amanto and the inhabitants had no choice but to accept these new outlanders as their new neighbours. It depicts Edo after it had been conquered by the aliens, and how it looks after they brought modern-day technology into a samurai country of ages past. Most of the story in Gintama is set in Edo itself, or in the sky above it, but the reader is also taken a few other places for various reasons.
Edo is the fictional city in which the protagonists of Gintama live and work. In real-life, Edo was the name of the Japanese capital Tokyo, before it was renamed in 1868, when the shogunate came to an end.
Snack Otose スナックお登勢, or 'Otose's Snack House' is a bar run by Otose, one of the 4 Devas of Kabuki District. It is a relatively small place frequented by Mu-san amongst others. It's regular employees are Catherine and Tama with occasional help from the Odd Jobs crew when they're late with the rent.
Kujaku Hime Kada's Casino, or gambling den, was one of many owned by her in Kabuki District. After the truth came out about her, and she was imprisoned aboard a Harusame Spaceship, it remains uncertain who took over her gambling dens.
Shinsengumi 真選組 being the largest organisation unit in the Gintama world as far as main characters go, have their own separate head quarters within Edo. This is different from the regular police stations which deploy 同心 doushin, who are dressed in the traditional Japanese clothes vs. Shinsengumi's more military-like uniform. Regular policeman would be characters such as Kozenigata Heiji 小銭形 平次, and the one seen in Episode 93 booking Space Woman for flying while drunk.
Yoshiwara Paradise 吉原桃源郷 is the underground red-light district that forms the backdrop for 'The Blaze of Yoshiwara First Chapter 吉原炎上篇'. Kamui 神威 is the current overlord in charge of this place under the jurisdiction of the Harusame 春雨 group, after its predecessor Housen 鳳仙 was killed in Episode 146. Previously perpetually covered by roof due to the overlord being of Yato tribe (and so having an aversion to sunlight), it is now open to the sky though the new overlord is of Yato blood too. In Episode 146 the new overlord was said to be totally indifferent to being the new overlord, and did not even station his men there, much less administer the district.
Yoshiwara and current overlord Kamui in the foreground.
View of Yoshiwara and overlord's mansion in the background.
The elevators used for gaining access into Yoshiwara.
According to Police Superintendent Matsudaira Katakuriko, Ryuuguujou or Dragon Palace City is a floating mobile city that operates as a high-class resort club for the elite class. It does not belong to any nation, and it operates outside any legislative confines, yet it receives tremendous support from the political world, to the extent that it has become very powerful. Since the Urashima incident (refer to Dragon Palace Chapter 竜宮城篇 for more details), it has descended into the depths of the sea and has remained there ever since.
Maximum-security penitentiary that resembles Alcatraz, but name is derived from 横溝 正史 Yokomizou Seishi's detective story with the same title, starring fictitious detective 金田一 耕助 Kindaichi Kousuke. Katsura Kotarou was brought to this place. Many of its prisoners attempted to escape at roughly the same time, resulting in the cliffs beneath the prison being dotted with holes. Despite it taking only a matter of days if even for Elizabeth to tunnel into Katsura's cell, prisoner's tunneling out have taken years, roughly fifteen in the case of the cell opposite Katsura's own.
The O-Edo 大江戸 (meaning 'Great Edo') Central Terminal is a large facility located in central Edo. It is where most of the spaceships in and out of Edo arrive and depart. It has been given an 'Architectural Landmark' status by the Bakufu. 
The Terminal is a large facility in the middle of Edo
The embassy of the Amanto species from the Planet Inui-sei 戌威星, which was the first Amanto race to descend upon Earth using military force, located on Earth. Featured as one of Katsura Kotarou's bombing targets.
The O-Edo General Hospital is a building featured in various episodes of Gintama. Whether it's the Yorozuya themselves who get ill or hurt, or they're visiting someone else who are, it's usually at the O-Edo General Hospital they end up. Notable employees there are the Staff Nurse 婦長 and Uchino 内野.
The immense influence and wealth of the Yagyuu Family, designated sword instructor to the Shogunate, is reflected in the vast sprawling grounds of the family estate. Many of the wings are made up of 2-storey buildings interconnected by sheltered corridors.
The Yagyuu Family's Crest at the Main Entrance
The majestic flight of stairs leading up to the Yagyuu Estate Main Entrance
The vast sprawling grounds of the Yagyuu Family Estate
Also acting as the Shimura family home, this dojo specialises in 天堂無心流 tendou mushin ryuu, aka Tendou Mushin sword-fighting style. Ever since Otae became the target of the gorilla-stalker, aka Shinsengumi's Commander Kondou Isao, the house compound has been fortified to become a fortress of steel. Examples of defense devices include steel-spiked wall enclosure, trip-wire with Justaway bombs, hidden ground pits with bamboo-spikes, gateways with massive timber cage-doors, toilet seats with thumb-tacks and also the ability to summon a satellite weapon called SOL 740 to fire a laser beam at selected spots. Refer to Episode 62 for an overview of the defense mechanisms at work.
Bird's eye view of Koudoukan
Example of Koudoukan's fortress-like defenses-steel spiked enclosure.
Shibuya Regret Hall 渋谷後悔堂 Shibuya Koukai Dou is a spoof of the real-life theatre 渋谷公会堂 Shibuya Koukai Dou, Shibuya Public Hall. Now called Shibuya C.C. Lemon Hall due to sponsorship deals with Dentsu and Suntory, the Gintama version sports a gigantic lemon logo behind the building sign. Featured in Episode 124 as the venue for Otsuu's live concerts.
View of the main entrance of the Shibuya Regret Hall
Kaientai 快援隊 comprises the fleet of spaceships belonging to Sakamoto Tatsuma 坂本 辰馬 that serves as his mercantile company traversing the galaxy, as well as the staff on it. Although Sakamoto is the leader, the company is mostly helmed by his second-in-command, Mutsu 陸奥, due to the leader's penchant for going missing-in-action.