Hillsbrad Foothills
Although Hillsbrad Foothills counts as a contested zone, quests in it are only available to Horde players, making it unlikely that you will encounter many Alliance players. Tin veins in this area are fairly clustered and mostly found close to mountains, both around the edges of the zone and along the mountain chain that surrounds the Ruins of Alterac. If you only have access to a ground mount, limit yourself to traveling in loops around the Ruins of Alterac. If you have access to a flying mount, you can travel on a wider loop covering the entire zone. You can easily reach this zone by traveling south from the Undercity. If you are using a flying mount you can fly in a straight line, while if you are on a ground mount you will have to travel through Silverpine Forest.
Northern Stranglethorn
Northern Stranglethorn is a contested zone and offers quests to players of both factions, making it fairly likely that you will encounter Alliance players. Tin veins are scattered throughout the zone and are mostly out in the open, although there are two caves you will have to dismount to navigate. This zone is very easy to reach for Horde players, thanks to the zeppelin transport between Orgrimmar and Grom'gol Base Camp. You can easily travel around the zone in loops on either a ground mount or a flying mount.
Ashenvale
Ashenvale is a contested zone with quests for players of both factions. The resulting likelihood of meeting Alliance players, combined with the zone's complex geography, makes it inadvisable to mine tin while on a ground mount. However, Ashenvale offers the highest amount of tin veins in the game, making loops around the zone an efficient way of gathering tin if you have access to a flying mount. Also, if your character is level 80 or above and you have installed the "Cataclysm" expansion, you can easily reach this zone by taking the portal to Mount Hyjal from Orgrimmar then flying directly south.
Stonetalon Mountains
Gathering tin in the Stonetalon Mountains zone is extremely inefficient if you only have access to a ground mount due to the zone's geography. On the other hand, this zone is smaller than most others and the tin veins in it are fairly clustered, allowing for efficient gathering loops if you have access to a flying mount and making it an ideal zone to gather in if there is heavy competition in other zones. To reach Stonetalon Mountains, simply travel straight south from Ashenvale.