On the East, Skaneateles is an affluent resort town on the North end of one of the best lakes. Many nice shops, Doug's Fish Fry (more than what the menu implies) is a great "joint".
Auburn is North of the lakes but close, it has an aging state prison, which is not usually a tourist destination but I have found that restaurants surrounding prisons are almost universally excellent. There is a Mexican joint North of the prison walls, an Italian place to the West, all superb. The architecture is good, it used to be a prosperous town.
If you aren't from the Great Lakes, go North to Sodus and Chimney Bluffs to see the real lake, Ontario. Wave to our Canadian friends....
Seneca Falls is a lovely little town with some interesting restaurants and a Hillary Clinton-approved National Park, called the Woman's Rights Hall of Fame. Eh I much prefer the Men's Rights Hall of Fame, it used to be a bar down the road. The North side of town is English, the South is Italian. There are interesting clues and political tension between the two groups, plus the Seneca Indians from Arkansas actually own the land underneath the town... reading the roadside protest signs is fun.
Down 5 and 20 on the way to Waterloo is Mac's Drive In, a classic 50s outdoor diner well worth the stop. The waitresses wear plaid skirts and roller skates, the root beer is in a barrel and mugs are frosted. But it's messed up, they have grease fires, they serve fried dough, weird stuff like that. Not like Sonic.
Geneva is home to Hobart and William Smith Colleges yet is a divided town between a rising meth/crack/heroin using population. Good for photography but maybe not for a family visit?
Canandaigua is maybe the prettiest town with the best architecture, a great pier, nice parks, shops, food... but the heaviest traffic.
You might as well go to Rochester and have some greasy garbage plate and visit the George Eastman House. I am such a community booster haha, there are fun festivals every weekend and plenty of fine food.
Further West is Letchworth State Park, the grand canyon of the East. It's a nice park in general, don't expect an Ansel Adams experience though.
To the South, I prefer Stoney Brook State Park to Letchworth for swimming, it is a nice walk along the gorge and has a lot of nice waterfalls.
Naples, south of Canandaigua, is maybe the nicest Finger Lakes town, compared to Watkins Glen to be honest. Not too large, nice park downtown, etc.
Watkin Glens, you'll see.
Corning has a cute, prosperous downtown and the Glass Museum is world class, with lots of interactivity and educational features.
Ithaca (home of Cornell) is an interesting town full of aging hippies and overly-PC college intellectuals, it has a vast array of restaurants... the Moosewood is famous for its vegetarian cookbook.
On the way North on Cayuga Lake, East side, is the town of Aurora, home of Wells College. It is a very photogenic and lovely little community. To the North is the McKenzie-Childs female mecca, try to leave the ladies off without credit cards.
The wineries? There are some very nice ones, but many are just fancy barns and sell raspberry wine.... so pick and choose.
I skipped Keuka Lake which is great, and dozens of other great spots. You could choose to visit waterfalls for days....
