I love Maine, and while I have only ridden around Bar Harbor due to just getting the bike this year, there are a million places that I think would be great to ride. Augusta should be no exception, and it has access to both the hinterlands in the interior, and the Downeast coast regions. Augusta is not a big city though, heck even Portland feels compact/small.

A good link is http://outdoors.mainetoday.com, they have a very good outdoors section which includes many cycling links.

Did I mention Maine is really big and parts of Maine are really hilly? And it has has 3500 miles of coast (if you go around all the points that jut out)?

I might suggest finding a route where you can ride under the gaze of Katahdin, that'd be pretty cool and not too hard to do from a good chunk of the state where it rises up prominently from anything else nearby. It's also not far from Augusta. Another suggestion is what my husband and I call "Moose loop" around the Carabassett Valley/Rangeley/Flagstaff lakes area.

One thing to keep in mind is if you ride in the hinterlands you will likely encounter logging trucks and/or farm equipment on roads. And a lot of roads are dirt, so you need to plan your routes appropriately. If you go along the coast, you will encounter tourists (potentially NJ/NY/MA bad drivers) in SUVs or RVs. Just meant to help you think things thru. The farther north and east you go, the fewer tourists you'll encounter. They spread out pretty well past a certain point.

Here's a bunch of stuff from the MT site
These are a few of the many organizations that lead bicycle tours in Maine:
# Can Am Wheelers are based in Norway, Maine and lead tours in Maine and Canada.
# Maine Wheels Bicycle Club organizes the Moose Tour, from August 4 - 9, 2002; and the Coastal Tour, July 14 - 19, 2002.
# Bike Riders Tours lead at least two Maine tours.
# Summer Feet, Maine Coast Cycling Adventures, is based in Portland and leads tours throughout the state.

Guides to cycle touring in Maine:
# Bicycle Coalition of Maine
# The state Department of Transportation has a list of 25 bike tours, including trail routes and detailed descriptions, that provides information on where you can find bike shops, accommodations, points of interest, places to eat and more all along the route. The routes vary in length from 20 to 100 miles long.
We've got a sample tour, the Portland-Cape Elizabeth Lighthouse tour, plus you can get all the details of the other Bike Tours in Maine on the Office of Passenger Transportation, Bike and Pedestrian Section Web page.
# Adventure Cycling Association has useful information, route guides and maps.
# The DeLorme Maine Atlas and Gazetteer is a great map resource for cycling in Maine. You can purchase it at most book shops and online at DeLorme.
# "25 Bicycle Tours in Maine," by Howard Stone, is published by Countryman Press.
# The East Coast Greenway explains its plans for a bike trail from Maine to Florida.
If you want a cool trip, you might consider Bar Harbor + The Cat + your bikes to nova scotia, and then ride around there. I know, not Maine, but you could very easily do a coastal route from inn to inn or something, and the towns in NS are just gorgeous. You could do a few days or a week. Unfortunately you'd need passports now....