Until the Fleet Starbase gets it's Transwarp conduit it can be quite a trek from Earth or elsewhere to reach the starbase for a visit or to do the Officer of the Watch dailies, particularly for lower level players without slipstream.
There is a bit of a shortcut though. If you take the episode "Night of the Comet" and keep that in your mission log you can transwarp to that mission's start location any time (Bepi 113 System.) From here it is just a short trip to the Starbase.
Costs 500ec and you need to be at least Lt. Commander (15) to pickup the episode.
This is the shortest route I have come up with, perhaps there are quicker ways?
EDIT: If you have rank 2 of Diplomacy from Doffs etc then you can Transwarp to K7 and head to the Fleet Starbase from there (Thanks Def Munky)
EDIT: This method of using episode transwarps can also be used in gathering commodities etc for starbase projects. These can often be purchased cheaper at different locations than if you simply replicate them e.g. Industrial Energy Cells are cheapest on Vulcan. If you take the "Diplomatic Orders" episode, you can then transwarp directly to Vulcan to go buy them.