I ended up in this current position because I was first interested in their field of work (geospatial work), and secondly skilled in programming. Even if I weren't a programmer I would probably work for them in some other capacity.
I don't feel qualified giving advice but personally I think I would look beyond what is commonly considered "tech". As another poster mentioned, everyone uses tech. When a company's work is sufficiently complex or special, chances are they may not rely on external vendors 100%.
Really out of my depth here but maybe some types of firms where I think there could be some interesting stuff internally:
- engineering
- analytics
- games
- graphics/animations