what kind of cable
I bought my daughter a blueray player, but the HD tv I'm hooking it to is old and does not have an HDMI port. Can I get an adapter to hook it up with an HDMI cable
If the TV is old enough not to support HDMI then it is unlikely to have the resolution to support Blueray. You will not see the improved quality offered by Blueray on a TV that only supports lower resolutions. You can still watch the DVD but it will be at HD resolution or lower depending on the resolution of the TV.