I am going to be flooring my living room in the next month or two with engineered hardwood and am at a loss of what to do around my fireplace. This is a corner stone fireplace and I have no idea what to do with the flooring around it, should I try to undercut it? quarter round with caulking? I want the best possible look that I am able to pull off as an amateur installer(2 rectangular rooms down!).

Here is a photo, forgive the Christmas mess.

What type of stone is it? Undercutting the corner area could be tricky. What direction will the floor be installed in relation to the fireplace?

undercut it with a crain jamb saw with a diamond blade and a good vacuum for the dust. fein tool the inside corners.

I am not too sure on the type of stone to be honest, it came with the house. As for direction the short side of the wood will be on the wall in the left of the picture.

I know everyone recommends crain saws but I found this available for rental at home depot and it looks like they make a masonry blade I can get for around $6.
http://www6.homedepot.com/tool-truck-re ... Saw/10-55/

Since I cannot get into the corners should I just try to chisel them out or maybe a handheld grinder? I will be pulling up all the base boards which will give me a little bit more room back there, but not much.

The only problem you will have with a hand held angle grinder is you won't be able to get the blade low enough while parallel to the floor.....you will be cutting at a slight angle. If you use the angle grinder get a diamond blade. You can use an oscillating multitool with a diamond blade to do some of the cutting. It will be dusty cutting the stone so cover everything up and you might want to have a helper to guide the dust collector nozzle.