What's the best way to plan out a long bike trip?

In about a month ill be biking from Boston, Mass to Miami, Florida. I'm wondering what's the best way to plan the route out. Any good iPhone apps that give you good step by step directions like a GPS? Take it day by day? What do you think?

I think you need to talk to biking clubs and even look at some of the guide books (older) you can find in the library. Riding safely on the East Coast is going to be a major challenge - often forcing you off the more level routes where main highways ban bikes up into foothills or longer routes around water features in shore line.
I would say the most important planning is where you are going to be staying each night - what your stages are.
Are you going to have a support vehicle? Spare tubes and tires and camping gear.

The best advice that I could give you would be to drive every single mile of your route first
Simply bc a website says that you CAN pedal a route doesn't mean that you SHOULD pedal a route
As Mike correctly noted until you get into VA you are going to be cycling thru the most congested area in the US and planning is going to be everything
To the best of my fairly extensive knowledge the George Washington Bridge is your only way across the Hudson as a pedestrian or as a cyclist
To get there w/o getting mugged in the Bronx do your E/W traverse as close to the Westchester / Bronx County line as you can and then head down Broadway to the GWB
Once in NJ I would head for Cape May
then
Take the Cape May / Lewes Ferry across the Delaware
then
Down the Delmarva Peninsula and at the bottom of it there's a ferry that will take you to VA
then
I would go down the Outer Banks
Ferry from Hatteras to Ocracoke
Ferry from Ocracoke to the Mainland and then follow the Atlantic to Miami
Here are two tricks from an old hiker
You go FROM where you spent last night TO where you're going to spend tonight. Sometimes that results in you meeting your planned miles per day and sometimes it doesn't
Have Zero Days in your planning
A ZD is a day where you travel Zero miles Sometimes the ZD is planned and sometimes it isn't But they always happen and you have to account them

Google maps has an option to map out a route for a bicycle.

"Map a ride.com". Have it set on bicycle mode and it'll keep you off roads bicycles can't go on. Also, what works the best is Just get a "Garmin", and make you route along the way. You might be told about something along the way you don't want to miss. I rode coast to coast twice the last 2 years and that's the way I did it. Also, on Map a ride, it'll tell you the steepness/grade of the road you'll be on so you can avoid the really bad ones. But, you don't have the Rocky Mtns or Sierra Nevadas in your way on the East Coast! Travel light, it'll make your ride more enjoyable! UPDATE: Don't ride at night, there's drunks and idiots out there. Also, check out some of the rode with Google street scene, so you know how much, if any shoulder on the road for the bicycle to use. Other than Mississippi (6 to 12 inches in plenty of areas), most road in the country are fine.

I think everyone has given you some sound advice. I would only add there are miles and miles of highway in your path
You can be peddling along on your merry way and suddenly you have encountered a bridge or a freeway that states no bicycles allowed.
Now you are stuck having to retrace your path for who knows how far
Something else some states have a law that if there's a shoulder you must ride on that shoulder. The problem is some states do not specify what the shoulder is. It may be a 6-12 inch piece of asphalt as someone stated with a white stripe breaking it and the road or it can be a 6 ft wide piece of asphalt and a white stripe. You need to know
Personally, with todays times I would take a CHL class and find out what states honor it on your path and carry weapon. You may encounter rabid animal, or just a plain mean one. You could use it to attract attention if you were hurt and knocked away from the road and you could need it for self defense period
You stop because you have a flat, it is late in the afternoon and no traffic. An animal out of no where or a couple of thugs stop and confront you