They were used for the markets and the trading centers of the city, and Jak often wound up in the Bazaars during the game.
The East Bazaar was not destroyed in Jak 3. It is seen still standing in the intro movie and from the KG War Factory. The KG Death Bots even concealed a wall from the blocked entrance to the East Bazaar (double-blocked). Since the bazaar has been abandoned since the palace's destruction, it is one of the only locations in Jak 3 to have no lights whatsoever.
Moving to the West Bazaar, it was completely destroyed either by the palace or Metal Heads. It was rebuilt along with the South Gardens (which was destroyed) to make Metal Head City and the Metal Head Tower. If you look closely from the KG War Factory towards the Metal Head Tower bottom, you can see some wood and an awning leftover.
An area of Haven City to the right of the Haven Palace. It was home to Onin's Tent before she moved her tent next to the Krimzon Guard Fortress and is a major center of trade in Haven City. It is also where citizens lived (as seen on the tops of vendors, there are small apartments). All vehicles were restricted to a single elevated roadway, making it easier to fight the Krimzon Guard here as there is no threat of attacking Krimzon Guard Vehicles. It was once ambushed by an Eco tanker hijacked by Metal Heads and was home to a battle against them.
The West Bazaar was the second bazaar area of Haven City it consisted of nine interconnected sections and was used as a trading area. Bordering the city wall, the Palace, the Northern Gardens and Southern Gardens, it seemed to be a central intersection of traffic. The West Bazaar was also location of Brutter and his Trinket stand (possibly also used to sell fish). It has no real importance in Jak II other than one mission located there. (rescue the Lurkers).