In Islands of Adventure (IOA) Spiderman definitely, not scary and it is just a ride that has a moving car that moves you to different rooms and movie sets, there are large screens that project 3-D film that interjects with some live sets and action. Great ride and not scary, no drops or anything. There is a simulated drop at the end but its just on screen (a movie) and you can even close your eyes on this if you get scared, because you don't really drop.
If you like boat rides the Jurassic Park River Adventure is one of my favorite, and sometimes I decide it is my favorite ride in all of IOA depending on what mood I'm in.

It is really cool for the most part you float down a peaceful river and animatronic dinosaurs are in the water beside you. THere is an 80 ft. drop at the end, but I think you can handle it, its not scary IMO.
Poiseidens Fury is a pretty cool show inside the Lost Continent area in IOA, just a show not a ride, you should be able to handle this no problem.
Suess Landing has some cute kiddie rides if you would like to experience what its like to live inside a Dr. Suess book, very cool area, and not scary at all, not thrill rides here.
There is a great log flume ride and raft boat ride in the Toon Lagoon area at IOA. You get extremely wet, but I don't think they are really "thrill" rides per say. The log ride does have a few drops but nothing major, but you may want to check this out before riding, it is probably the most thriller of these rides I've mentioned and may be iffie for you if you don't like drops and fast rides.
Plus all the rides the other poster mentioned at the main Universal park are great and not thrill rides.
IOA is a beautifully themed/landscaped park with 6 different lands/islands. So you can actually just walk around and eat, and soak up the scenery, (I do this all the time.) and you will not get bored just exploring. Its probably the best themed park in the world IMO.
Also, I would suggest if at all costs you can muster up some courage and ride the Mummy, it is a bit of a thrill ride (it gets fast at the end) but its not like a regular roller coaster (no big drops), and it is very cool. If you like dark rides (kind of like Haunted Mansion or POTC at Disney) it is very cool, a little scarier though, it is my favorite ride at the old Universal park I would highly recommend you doing this if you think you can do it.