Do you have early entry and the willingness to be at the gates at least 30min before early entry starts? If so, start with Islands and go to Hagrids first. (Assuming early entry remains at Islands in June.) If Hagrids is down at park opening, immediately switch to Velocicoaster (it's on the way). Otherwise, ride Hagrids and then immediately go to Velocicoaster. Velocicoaster does have a single rider line which is highly variable depending on the CM - whether they're pairing the odd parties or not. Hagrids also has a single rider but you'll generally be in the sidecar. Both single rider lines are closed fairly often.
Kong would probably be next, it claims to have a single rider line but I've never seen it available. Spider-Man & Hulk both have pretty quick single rider lines.
Are you doing the water rides? Fair warning, you will be soaked.
Alternatively, hop on the Hogwarts Express to Studios after Kong or after Velocicoaster - earlier in the day, the train will have much lower waits than in the afternoon. Early enough, and the Gringotts line won't have built too badly yet.
If no early entry, start at Studios - Rip Ride Rocket or Gringotts first.
At Studios, clockwise from Hogwarts Express:
Gringotts - good single rider line, however if you haven't been on, it does skip all the pre show and back story, and the queue is impressive, so you might want to do the regular line? Particularly if you are a Harry Potter fan.
MiB - single rider is crazy quick, almost always a walk-on.
ET (are you considering this a kiddie ride?) - no single rider line. May not open until 10am (Simpsons & DreamWorks area also may not open until 10am).
Honorable mention - if you have time, the Bourne Stuntacular is really fantastic show! And it is a good AC break.
Rip Ride Rocket - single rider line is generally slow, and queue is hot & boring.
Villain-Con - no single rider, this is arguably not a ride but you stand a moving walkway from which you shoot virtual targets.
Jimmy Fallon and Fast & Furious - no single rider lines (rides are meh).