Dedicated line questions...

If its exterior or underground 10awg (gray color) no need for conduit. It could be tucked up along the skirt of the house, or under a deck, and positioned where no one would see it. Maybe you can find a good place to transition in? Good luck...

It was a lot easier for me to run my dedicated circuits. I ran 6. You don't want to have dimmer switches, or other appliances on the same audio circuit. I live in a log home with a crawl space. You can actually walk in when entering, then it becomes more of a crawl. I ran my 10awg (exterior wire) from the breaker box, 6 20amp breakers, carefully stapled the wire to the floor joist. I had drilled the holes close to the exterior log wall, pushed all the wires through the pine floor, make sure you leave enough on each end. I used Furutech NFC Rhodium outlets. I even soldered the ground connector, and spade connectors as to have a proper contact. OCD all the way! I just mounted the junction boxes to the wall. I wrapped all the wire in black. what you do see has a retro look. With drywall or fishing wire through it would be a lot harder to do! All these things, cables, outlets, dedicated circuits are accumulative. If you have a revealing system all these things make incremental improvements. 

That's the difficult part. As mentioned myself and some others on this thread have crawl spaces that make running the wire a lot easier. I don't know the layout of your house, but I have heard of guys running external 10awg and navigate the wire from the outside in. 

Just run 10awg from a 20amp breaker to a quality outlet. For my monoblocks I only use one inlet per outlet. I'm able to this because I wanted more than enough outlets. I separate analog/digital per circuits. This is not that difficult.