So you have taken out a wall where there were hardwood floors on either side. You know you have to fill the gap with something, but what?
The first realisation is that even if both sides are floored with the same wood installed at the same time, the boards on one side will never line up with the boards on the other side. You cannot just continue the boards across the new room. I think that the best solution I have seen is to trim both sides straight and insert new boards perpendicular to the old ones, often going for a totally contrasting wood or contrasting colour since you simply cannot match the old aged wood.
The easiest way to cut really straight lines in a floor is to make a simple jig. Start with a piece of masonite about a foot wide. Screw and glue to it a piece of half inch plywood about 6 inches wide with one very straight edge which goes in the middle. Make sure that your screws are countersunk so that they will not scratch the floor below. I always put the dimpled side of the masonite down (it will sit on the floor) and the smooth side up where the plywood is.
Now put a good blade in your saw and be sure that the saw is well adjusted to 90 degrees. Set the shoe of the saw on the masonite with the shoe up tight against that straight edge of the plywood. Cut all the way across your 4 foot or even 8 foot jig. That will cut off the excess masonite and create a very accurate guide in that the cut edge is always where that saw will cut. You can simply line this edge up on your cut mark on the floor, make sure that the jig is properly weighted down (because you can't clamp it to the floor) and cut just barely through the total hardwood thickness just barely grazing the sub-floor.
I usually open up this slot wide enough for full pieces of hardwood to fill the joint, rather than having a strange looking half board on one side. You may need to do some more similar trimming elsewhere in the floor to balance the design if it looks strange all by itself in the middle of the room.