Rough Timeline of Tim Drake's Home/Schooling
Tim starts his life living in Coventry in the Robinson Penthouse/Condo. (Headcanon until I can find more confirming info.)
Tim attends a boarding school specifically outside of Gotham. He boards there.
Once he moves in with Bruce in Bristol he attends Gotham Heights High School.
Then he moves back in with his father into Drake Manor (Bristol Township, Crest Hill).
He continues at Gotham Heights at Drake Manor.
Drakes move to Keystone during No Man's Land and upon returning he gets transferred to Brentwood Academy, the boarding school outside Gotham.
Then they lose their money and move to a condo down in Old Gotham near the Clocktower and Tim transfers to Louise E. Grieve High School.
Blud Arc (?) (Find more details later)
Bruce adopts him and he attends Gotham City High School in Diamond District. He drops out from here.
Corrections provided by @katanahime. Thanks!