It took me 1 1/2 days of driving to get from NH to Columbus OH choosing the northern route with overnight in Erie area. Lots of vineyards. From Albany NY to Bennington VT, and nice drive to Keene NH area.
From Keene you can take route toward Concord NH. In the Concord area there is at least one kayak rental place. The Merrimack River is a great spot. They'll drop you off and pick you up. You can picnic at a secluded sandy beach along the river. Great bird watching and chance to see bald eagles.

Head north on I93 and choice of any White Mountain attraction or hiking. Take Kancamagus Hwy east. From the Conway area it's an hour to Portland ME. Take mailboat cruise of harbor, perhaps spend the day on Peaks Island which I've heard is great but we've just stayed on the boat. I think there's some scenic cruises to see lighthouses in the evening.

Then up I95 to Bangor. While in Bangor see Cole Transporation Museum which is more about work vehicles than classic cars. Check to see if there are any logging competitions going on but maybe not in August. One June we watched college teams compete at Leonard's Mills Logging Museum. On your way north from Portland you might want to stop at LL Bean in Freeport. Harraseeket gets good reviews on their lobster sandwiches.

On your return trip you might backtrack to Conway and head to Littleton NH then across to Vermont. The Great Vermont Corn Maze is a fun visit and good hike.
Over to Burlington VT. Check out the Intervale. I visited for Gardeners Supply but I think this is a popular biking/kayaking etc area. Take ferry across Lake Champlain. Possible stop a Ausable Chasm. Hike thru a gorge with boat ride at end.
Head back to Cleveland.

Even if you don't choose this routing, once you pick your towns do an in depth search of activities which might include on-line visits to local newspapers. There's a lot of local activities that only get a brief mention under Things to Do. I went on a terrific bird walk led by the local conservation committee. There might be some good church suppers in Maine on a Saturday night. One visit we discovered a benefit lobster cookout in the Rockland area. Really good deal on lobster and mussels to benefit a local volunteer fire dept. Many towns offer free outdoor concerts. (Take a picnic supper.)

There are zip line tours in the White Mountains now. You would probably like that. If you have the time, include a visit to Camden ME and hike up Mt Battie. Take a picnic lunch and enjoy the view from the top. It's stupendous.

The fastest way is on either I 86 or I 90 east to 495 to 95, but going through the mountains in VT and NH as dfrostnh suggests would be more interesting.

For things to do in New England go to www.visitnewengland.com/

I live in Southern NH and make the trek to Cleveland at least twice a year so I know the three main routes quite well (I-80, I-86/I-88, and I-90)

I-86 from Erie to Binghamton and I-88 from Binghamton to Albany is more scenic than I-90 from Buffalo to Albany (unless you plan to add Niagara Falls on to your trip). Like other posters have said, shoot up to Schenectady and take Route 9 across Vermont to NH.

We did this drive from Akron to Acadia National Park many years ago. If I remember correctly, we spent 2 nts somewhere in the Adirondacks, crossed Lake Champlain on a ferry, spent a night in Stowe, Vermont and then headed to Acadia. Coming home I remember we went south and then headed west so we could stop at the Baseball Hall of Fame in Cooperstown.

So many ways to sightsee or just hustle on via interstate. dfrostnh has outlined good route. To Bangor to see Stephen King's house? Really! Mentioned already is Leonards Mills Logging Museum and LL Bean but not mentioned so far is Acadia Nat'l Park not so far away...or American Folk Festival weekend of Aug. 27 which we hope to enjoy.

Part of the fun though is planning so figure your own route. Lots of fishing and hiking spots for example...just keep searching or rather just look around when in Vermont.

Bill in Boston

Are you planning to drive straight through to Bangor or are you taking it slowly?

There’s the obvious fast route, taking the Interstates from Cleveland to Bangor, then there’s the scenic route. The scenic route will add some time to the drive but you’ll see some nice sites along the way.

Have you ever been to New England before? The drive through VT and NH to ME is nice with mountain views. Fishing is easy to access and there is plenty of hiking along the way. If you look at the maps and drive through Rutland, VT you will drive by Killington, VT on Route 4 into Woodstock, VT. Woodstock, VT is a nice, although expensive, town. Be sure to abide the speed limit in town. Continue on Route 4 to Route 89 south, take Route 91 north to Woodsville, NH. Take Route 302/ 10 to NH Route 112 east. This is the west end of the Kangamagus Highway. Take this into North Woodstock, NH. This is a small NH village with a few restaurants, Truants Tavern, and The Woodstock Station and Brewery, and shops. Continue to Lincoln and onto Conway, NH. You will be driving through the heart of the White Mountain National Forest. There are so many hiking trails here you need a guide book. First, stop into the Mountain Wanderer book store in Lincoln and ask the store owner, Steve, for some hiking advice for a trip to suite your time constraints. If you don’t have time to hike try to arrange the drive time during daylight to see the views, they are amazing.

Conway is not too much but does have a great Mexican restaurant, Café Noche, right on Route 16. Aa little north on Route 16 is North Conway. This is another touristy New England village. There are also tons of restaurants and shopping outlets. I ignore the outlets and go the center of town. There are good restaurants here too, Rafferty’s and Horsefeathers.

It’s about 3 hours from North Conway to Bangor. You’ll be seeing the back woods of Maine and opportunity to see moose.

In Maine you have to visit Belfast, Camden and Rockland. These are all on the coast on Route 1. Route 1 goes from Key West, FL to Madawaska, ME on the Canadian border.

On the way back you could stop into Cooperstown, NY and visit the Baseball Hall of Fame. This takes a whole day to appreciate.

Regards