Get the nigiri and of that, get only the cooked items. If you dont like raw fish though, enjoying the full range of sushi items can be tricky.
You might like the Tamago nigiri, which is a cooked egg custard. The Ebi (shrimp) nigiri is cooked so that works as well.
Is it just the rolls wrapped in seaweed you do not like? If you get the maki rolls those are wrapped in rice with a thin layer of seaweed between the rice and fillings. It would be hard to discern that flavor for a lot of people. If you can stomach it, there are various vegetable maki rolls that make prodigious use of ginger, cucumber, scallion and the like.
Do you like smoked salmon? Most places will have that as well.
Finally, if you like a place sit at the sushi bar and talk to the guy behind the counter. Once you get to know them, they will be very helpful in steering you to your preference.