I'm hoping to collect some beta for recent graduates looking to continue with their ice climbing. Let's have your suggestions here. I'll start with some TR advice:
Top-Roping
As Will Gadd points out, Ice-Climbing is NOT Rock-Climbing, and lead falls often have serious consequences. It's a good idea to spend some time on a steep-ice TR apprenticeship to make sure you're solid before you try and advance into leading. It has worked for some of the best: supposedly Will Mayo taught himself to climb ice by running TR-solo laps at Lake Willoughby. As an added bonus, you don't need to go out and buy ice-screws, and multiple climbers can share a few pairs of ice tools. If you're psyched on it, think about organizing a TR day during one of the Open Cabin weekends.
Where to Go
TEXACO, CHAMPNEY, ARETHUSA and CATHEDRAL NORTH END are all great TR crags, and there is plentiful information on each of them on Mountain Project. Two other places to keep in mind are THE FLUME, and KINSMAN NOTCH. As these are located in or near Franconia Notch, it is a shorter drive from Boston, and suitable for day trips. If it stays cold down south, AUBURN ICE CANYON is another great spot with a much shorter drive. Because they are great TR crags, these locations are also fairly popular. Bite the bullet, wake up early, and get your ropes up on the goods stuff. Don't be intimidated by guides and such...you have just as much right to be there as anyone...but of course it is always good karma to share ropes if you can.
One note about etiquette. If climbs are building (e.g. a currently thin pillar), it is nice to avoid knocking it all down (drop your ropes on the fat stuff instead), in the hopes that the climb might form later in the season, allowing everyone to enjoy it. Towards the end of the season this is less critical.
If you're feeling adventurous, various other crags exist, and some are quite nice on the right day (usually uncrowded). Look through mountain project and the guidebook (An Ice Climber's Guide to Northern New England, available at IME).