I just backed up my Wii using Bootmii, and now I have a bulky 500MB NAND.bin file on my SD card.

My question is, to save space, is it okay if I move the NAND.bin file to my computer untill I actually need to restore my Wii (if I ever have to that is)?

Yup, just remember where you put it ;)

Okay, and then also is it okay for me to sometime in the near future write a new NAND.bin (after copying the old one to computer) for the purpose of updating save game files?

Yes

Indeed, you should backup NAND regularly to ensure you have recent game saves and any newly downloaded channels (i.e. VC/WW games).