There are a few off-site parking lots. Park Place and Park n Fly are two that we've used. You have to take a shuttle to/from the airport maybe adds 10 or 15 minutes to your trip and they're the cheapest. The onsite budget lots are almost always full but the covered short term parking is usually available but I think is up to 20 bucks a day. The airport lots charge you for a full day even if you're 5 minutes over the 24 hour mark. Have a fun trip.
Airport Fast Park. I think I pay like $10 a day when I park there. It's under a canopy so your car stays clean of snow and rain, they'll give you a bottle of water on your way out if you want, and the shuttle is literally waiting for you at your car when you get out. I feel bad at times because it's sitting there as I change my work boots into shoes and grabbing my bags. The airport keeps changing the drop off location for the shuttles with all the construction but it's a fairly quick walk wherever you need to go. Since they all charge almost the same amount, I go for the covered friendly option.
When I used to fly on the company dime I always tried to park under cover at CLE after I landed at 2 AM once and found my car sealed in an inch of ice from freezing rain. Given a choice at that airport always go with the roof from November to April. I didn't know Fast Park was covered.
I live close to the airport so I can easily UBER/LYFT or get dropped off there HOWEVER when I lived in Youngstown I always used the recommendation above. You can also make a "reservation" on the website and apply a promo code (many found online via a Google search)----its easy surface parking and the shuttle comes around all the time to pick you up. Its literally a 3-4 min ride to the airport.