I drilled holes in the ceiling of my rented house to run cable through the attic and down into separate rooms. Never heard anything. Don't need a big hole so it's easy to patch when they come through for nail holes and such which are expected.

Sometimes you can have great success using the wires that are already in your walls, provided it's in good nick and isn't isolated. Try a powerline adaptor.

Otherwise, do like i did and run a 50m cable halfway around the house.

Protips for diy renters: you can buy conduit baseboards. They're baseboards that have a void behind them for cabling. If you're good with tools, you can remove the existing baseboards and put those on. When you leave, either replace the original baseboards or just pull the wires out and leave them there....

What I did was use cup hooks to put wire along the top of walls. A small step stool helped me get up to the ceiling line, put a nail partway in to get a "pilot" hole, then screwed in the cup hook... did one hook every 18-24 inches about 2 inches from the ceiling. With larger cup hooks, I easily fit 4 ethernet lines in. I also got some wall mount wire conduit to go down the wall to my router. For doors and such, vertical wall mounted conduit to the hinge, under the door at the hinge, then back up the wall on the other side to the ceiling to continue (or along baseboards to the device). I only had trouble with the vertical conduit (I only had one) when I left since it was attached with mounting tape.

My way was pretty clean, never had to look out for cables on the floor, I didn't really notice them at all, and all the important stuff was wired.

If you're just going between neighboring rooms (eg. Your router is in one bedroom and you want to get to the bedroom next to it), look for telephone/cable TV hookups. If there appears to be one on both sides of the wall in the same spot, open it up, there's a good chance the wiring box for those lines goes straight through the wall. If you want a more professional look to it, buy keystones and use a short bit of wire to link two together, and just put them on either side of the wall using Keystone faceplates... so you can just pass the cable through the wall....

There's also MoCA if you have coax in every room. Look it up, it's great.

There's a ton more I could say on this, I'm a big believer and advocate for ethernet over WiFi, because after spending a long time working on WiFi professionally, I've realized that all wifi sucks. My mantra is "wire when you can, wireless when you have to". If it's feasible to run a wire, do it. For mobile and non-stationary devices, wireless since those move around and it's impractical or impossible to put ethernet everywhere it could be.