I used
Aurora for quite a while. It also functions as a sleep timer, etc. Has multiple alarms, all that.
I think the new version (v.4) is no longer free, so if you can find the old v.3, that is ultimately best. Works well, and has a failsafe or two (but still, be damn sure your MB is set up so that it WILL make noise no matter what...
[EDIT]
Oh, missed the part about displaying time on screen. Aurora doesn't do that, but not sure what will... not to mention, since you would be using the display's backlight, it will end up being a bit too bright to really leave on all night (unless you need yourself a night light too, lol
)
Also, the v.3 download is still available on that link I provided. That should be the freeware version, not shareware!
[/EDIT]