Yes, there are gourmet burger places, and some fancy restaurants serve burgers (I've had a burger in a Jamie Oliver restaurant for example).

What do you consider better than a burger for fast food though?

You can get burgers at sit-down restaurants. Famously Red Robin. It's a non-fast food burger restaurant.

There's a gourmet burger restaurant near me. Semi fancy sit down enviroment.

Square1 Burgers and Bar. They named themselves that because they took making a burger back to square one

There are some "craft" burger chains like The Works, don't know if that's only Canada. A burger you get a steakhouse is usually going to be much higher quality too, ground in-house cooked medium rare kind of stuff.