I have almost the exact same year Honda Accord. If you do want to keep your existing Alpine unit, you can buy a third din attachment kit and put a flip up monitor in there.
There are a few other people on this forum, that I have seen, that has the same generation Accord and they usually fabricate the bezel to fit a 7" monitor in there. IMO, I think that way looks the best. A little cutting and bondoing is all that is needed; nothing major.
As for PC locations.......I think that the trunk is one of the best places to put it. It allows for almost any type design to be implemented without the hassle of trying to save space. Cooling would probably be mush easier to achieve in the trunk since it is in a more open area. Others have put the actual PC components in-dash too.