Most of the time you spend leveling will involve questing and slaying monsters, but there’s also a lot of travel. Travel earns you little experience (you do gain a bit for discovering new areas), so it’s wise to keep travel to a minimum. The new level scaling system, which scales zones to your level within a preset range, helps with that. You can choose what zones you want to experience and stick with them until you finish their quests.
Obtain your heirloom rings. Ghost Pirate Rings can be obtained via Shipyard missions. You can equip one ring from this category. A Dread Pirate Ring can be obtained via placing at least second in the weekly Stranglethorn Fishing Extravaganza, which on many realms is a very competitive event. Note that to obtain the Ghost Pirate Rings, you will need a max level character with a garrison of at least level 3. You you will also have to develop your Shipyard to the appropriate level to receive the mission. Your other heirloom gear will still give you a big boost if you choose not to go for these.

Usually it's best to avoid a lot of instance runs. It is too difficult to account for bad groups, and some instances are too far away with too few quests. Since the experience is very good, it's a good idea to clear nearby instances which have a lot of quests once (Gnomeregan, Deadmines for Alliance). Distant instances with few quests should be avoided (Deadmines for Horde). Low level instances can be cleared by paying or befriending a single high level character. However, since patch 3.3 a new Dungeon group finding system has been implemented, as well as a direct port to dungeons (when entering the group you get ported to the dungeon and back to the same location if you leave it) and thus the travel time to dungeons has been greatly reduced. This makes it a good idea to complete quests or grind while you wait for a group to become available.