There is a school of thought that anything that tastes good on bread should taste good with rice.

Tried and tested ideas from my family for temakizushi are: avocado, smoked mackerel, prawns/shrimp (battered if you prefer), sliced cucumber*, omelet strips, kinpira (esp carrot and gobo - or substitute sunchoke/artichoke for gobo/burdock root, just beware the inulin flatulence.)
Tweaking further I’d add most kinds of soboro: salted salmon, canned mackerel, canned salmon, even canned sardines, and there is pork or beef too - the secret to soboro is how you season it, it’s generally salty from soy sauce/shoyu with sweetness from mirin &/or sugar, oyster sauce is a good secret ingredient for beef and pork soboro. You could fry thin strips of (or shredded) ham/bacon/pork belly with soy sauce, sake and a mirin/sugar to get a “tastes good with rice” result.
Also, rather than going for chicken katsu, I’d steer you in the chicken karaage direction - it’s yelling “hello!” at you.

Now if you want to go off in a completely unfettered, what can I eat with nori and rice direction, don’t get too shackled to the vinegared rice concept.

Take a look with Google images at onigirazu in Japanese おにぎらず or お握らず
hot dog wieners, ham slices, chicken nuggets, cheese, hamburgers - the “anything that tastes good with bread” concept is flying in Households throughout Japan. One only needs to free themselves from the binding dogma of osushi.

Nori rules!

* cucumber: I’ll take the ends off and grind ONE end in some salt for a minute to make it less bitter through the osmosis process. Depending on the cucumber, I might remove some seeds (this pulp can be added to a gazpacho)