So the hold bounties have started asking me to kill giants but I kind of like those big ol luggz. I have been avoiding accepting the quest but I was wanting to know is if I wait until I am a higher level will I start being asked to kill something other than giants?

Giants and bandits is pretty much it, Ive found.
I dont do these quests anymore, because I also like the giants.

The only thing that lets me do these quests is the Giants that you are tasked to kill are spawned in the camps (usually). So, I just RP that the Giant is a bad giant and needs to be taken out, but the other ones can be left alone.

Of course, convincing the other Giants in the camp to leave you alone while you are carving up one of their brethren is the trick.

ive gotten bounty quest's for dragons, as far as giants go...the only good giant is a dead giant

I myself only ever really get asked to kill dragons.

You can also be asked to clear a Forsworn camp, but it's possible that it happens only in Markarth. I don't kill Forsworn or giants, so I stopped asking for these quests long ago.