Advanced Travel Tips
Use a Super Group base
Get a good SG so you have base teleporters if nothing else (or make your own). Most supergroups love low level characters so they can get prestige to build their base so you shouldn't have trouble finding one.
If you don't know what I'm talking about, Super Groups are hero associations. Being in a supergroup lets you chat with other members of your group in a special channel and since the release of City of Villains, you can also have your own super base. The super base has many uses though the most important for me is that you can get teleporters in your base to just about every zone in the game making travel much faster.
Carry Awakens so you can rez without running back to missions. Being in a Super Group helps with this too since you can go to the base instead of the hospital and then right back to the mission door (or the same zone anyway).
Safeguard mission Travel powers
Safeguard missions are the Hero equivalent of Mayhem missions for villains. In them, you complete the mission by preventing a bank robbery. Your reward is a temporary power. There's a different safeguard mission for every 7 or so levels, but the point is that they're divided by city zone. There's an Atlas one, A KR, one, an IP one, etc.
Because of the new SafeGuard mission temp travel powers, if you do the Atlas and Kings Row you will have fly and super jump from very lows levels. Because of how long they last in tandem, you can focus on other powers and save your real travel power for much later. Shazel, for example, didn't need any travel power or travel power prerequisite up till level 30.
Jump Jet Pack and Pocket D Teleporter
If you never bought the special edition of City of Heroes which gives you the Pocket D teleporter, the Jump Jet Pack, and the extra costume pieces, you can buy those separately for $10. The amount of time you save in travel because of the Pocket D teleporter and Jump Jet Pack are worth it alone, but the costume pieces are much better than any of the Veteran Reward stuff (except wings of course). For low level travel (and even later), the $10 is totally worth it.
If you haven't heard about Pocket D, have someone show you. Many holiday events are held there, but more importantly, it connects several zones together providing an alternate form of travel. Right now, PD connects Kings Row, Founder's Falls, Talos Island, and Faultline. It's important for saving travel time even if you don't have the teleporter.
The jump jet pack is a power that when activated let's you jump in mid-air as many times as you want until the power wears off. It slows down your horizontal movement, but will get you out of crevasses and over steep walls. It saves a lot of time wasted due to falling in the wrong place.
Even better, if you have hover, fly, or the Raptor pack, they will be faster when the jump jet is active. A 30 second boost to your flight speed can get you across a zone much quicker.
Hospital Express
For low level characters, the best way to travel is often to die. For example, since you don't get Debt under level 10, dying gets you instantly to the hospital with no drawbacks. Faced with taking 5 minutes to cross a zone (or longer), dying is a quick way to travel if what you want is near a hospital.