I'll give you some 'tools' that will enable you to find a good majority of the aircraft based in the area. Here are 3 websites, the first is LAAS, a quick reference to corporate jets and turbos. The second is the FAA database, where you can look up individual numbers.
Then the 3rd Flightaware for CLE for business aviation, and CGF Cuyahoga County Airport. Now some aircraft are blocked, those you won't see, but click on any biz jet registration, on the new page will show the owner and the city the aircraft is registered. You can then enter it into the FAA database.
Note; in 30 seconds, I see N416BA, N530P, N155RJ, N4200, N5200, N247CJ, N316EC, N105CJ, N6100, all based CGF. Just enter each number in the FAA database, and you'll have the registered owner and contact address.
LAAS Biz and Corporate quick reference, you can enter any 'N' number into FAA site.
FAA Registry you don't enter the 'N', just the numer, ie: N234P enter 234P.
On the left, you can click aircraft type, enter any type, and the register will show every single aircraft of that type registered in the USA, then click on any specific aircraft - and you get the owners info. So you can enter Learjet, then look at the 45's, look for any based in Ohio. Click Ohio, and it shows each Ohio based Lear 45.
FlightAware for CLE , under arrivals, or departures click more; on the page that pops up click on General Aviation. There will be a couple days arrivals or departures, click on any registration, the new page will show owner, and where the aircraft is based. Any that show Cleveland - are what you want. Then enter the 'N' number in the FAA data base, you get owners address.
Cuyahoga County Airport FlightAware seems most of the biz jets are based here.
Good Luck.