Hudson owns no disposal facility, and Summit County has no publicly operated landfill or transfer station that can be named as the destination. The county health department reports that it inspects three active construction and demolition debris sites and three active transfer facilities in the county, but it does not name any of them, so the honest answer is that the destination is set by the hauler's own disposal agreement.
The City does keep track of it, and that works for you. Every licensed hauler has to state in its application where solid waste and recyclable material will be taken, and then report to the City four times a year with signed tipping tickets from the recovery facility it used. Your account manager confirms the destination for your load and the cost before delivery.
For the material that must not go in a container, the county's own site is the answer. Summit ReWorks at 1201 Graham Road in Stow, reachable on 330-374-0383, runs the household hazardous waste collection for Summit County. It operates seasonally, from June through September, on Thursdays from 2 to 7 p.m., and it is worth checking the season before you drive over.
Two limits matter. Containers larger than five gallons are not accepted, and the collection is open to Summit County residents only, with material generated at their own home. Business, school, non-profit and government material is turned away. So nobody should plan to arrive there with a container load.