Does it only have antenna input? I suppose home computers that only output a B&W signal (i.e. ZX-81/Timex 1000, Acorn Atom and so on) will look just as good on a B&W television as if the TV was in colour.
A lot of administrative software and text adventures for colour computers should also be fully enjoyable in B&W. Some games and software that rely on that you can see colour and not just shades of gray may be less playable. I remember my big brother playing Jammin! on the C64 in B&W, and it was a nightmare. On the C64, the sixteen colours roughly are divided into five shades of intensity, and on a B&W television it is almost impossible to see the difference between e.g. green, purple, orange and light blue. The mentioned game is based on that you should match objects with areas of the same colour, which makes it quite a challenge to play on a B&W TV.
