I'm actually trying to move to a HCOLA because I'll make a ton more than I am right now. Yes, I know the expenses will go up as well, but if you do it smart you can really do much better. I do plan on living with a roommate, in fact I already have a friend who is willing to share her 2 bdrm for me paying the same rent as I paid on my mortgage in my LCOLA. So there goes the biggest expense.
The city I'm looking at (NYC) I won't need my car, so I'll sell mine ($!) and switch to public transportation and walking/biking (yay health!). So there goes the next biggest expense. There isn't much I can do as far as groceries, or at least any more than I'm doing now (farmers markets, cooking at home, cheap staples in bulk), but everything else more than makes up for it.
Plus as someone above said, in densely populated areas there is so so much to do, a lot of which is free/discounted.