I'm planning my own fanfic and I'm wondering how far away has Starfleet gone from our galaxy by the 33rd century? What is the farthest galaxy they have visited and how far away is it?
It's up to you, really. Consider there was a huge temporal war in the 29th century so you could imagine that the Feds won and make regular trips to neighboring galaxies via Temporal Slipstream Drive or you can say they lost and the "federation" consists of Klingons, Cardassians, Gorn and their subject worlds. Fanfic is great, it's literally completely up to you.
Okay then. My plan for a fanfic is actually a crossover to a fantasy franchise, but I wish it to feel as much Star Trek as possible. I wish an UFP starship to go to the "galaxy far far away". But.... since fanfic is just fiction never intentioned to be commercial, I think it's more for the writer's entertainment. I'm going sloooowly while savoring every step, thinking it all over before writing a single line of story.