Vast majority of the time it is easier to run it either down to the crawlspace or up into the attic and then over to the next room, vs removing baseboards and trying to route around doors.
The reason why you cant find a good idea on cost is because it is very variable. First and foremost your house layout is a very large variable. If you have a crawl space and can just drill down from wall cavity, do the same and fish the wire then most any place should do this for less then $100, maybe even closer to $60. If you have to go up multi-story, have to go through insulated and fire-braced walls, and/or have a very limited access attic then the cost can go up to $200 easily because it is now a 3 hr job. The other variable is that each...