Hi C.,
I like the beach idea, there are lots of places to choose from, depending if you want ocean beaches or lake beaches.
You don't have to take your vacation in the winter. summer is a good time too, and it might work better with your schedules, since you and the 13 yo are in school.
Think about some of the national parks. We ( my parents, brother and I) liked Yellowstone so much that we made a detour on a subsequent vacation to go see it again. GRand Teton Nat'l Park is beautiful; also Mammoth Cave, Grand Canyon, Acadia--lots of them!
Ohio has some nice state parks too, where you can rent cabins (tents in some, if you want to try camping), or stay in a lodge (like a hotel). I particularly like Lake Hope and the Hocking Hills area--very pretty, woodsy, hilly; Geneva State Park is close to Geneva-on-the-Lake which is a family-friendly place (bills itself as being one of the oldest family resorts on Lake Erie, I believe).
We (my DH and two boys) enjoyed a few days by the ocean in Old Orchard Beach, Maine; although the boys were 5 and 2 at the time, not same age as yours).
If you really feel the need for a break during the winter you could take a weekend and go to an indoor water park like Splash Lagoon in Erie PA, or there are several in Sandusky OH (I don't know where you live). You'd still have money left over for a longer trip.
Do you have AAA? you could ask them for suggestions.
Don't try to cram too much in, save some time for just hanging out and enjoying each other's company. Pack a deck of cards and maybe some small games for some low-tech fun.
Don't forget the cameras! Have a great time!
K. Z.