Other than local (your home network ) name resolution, requests end up on the net, your referred DNS server (ISP, Google, etc). So there is really no right answer to this question.
I personally set-up my router to handle DNS forwarding to ASU (my local university, a good go to, lickety split) and Google. That is generally one configuration point, instead of a couple. I find it cleaner, and easier to reset if I lose the configuration on my router, or have to reset it.
If you want to do local name resolution you'll have to set-up your router to handle it, it tends to be optimized for that, and if possible cached.
Hope that helps.