Road trip from Denver or Salt Lake City?
 

Ok I'm in the beginning stages for a trip probably in early June of 2016. It will be me my wife and 6 year old. We're looking at the main thing being the Grand Tetons and Yellowstone. We'll likely have 7-9 days for the trip. I've been planning on a flight to Denver arriving around lunch car rental then driving halfway to Cody going thru Laramie snowy scenic byway to Rawlings then thru wind river canyon to Thermopolis stay somewhere in between Thermopolis and Denver probably more likely between Laramie and Rawlings.
Day 1.
Day 2 May spend some time in Thermopolis, see the Buffalo Bill museum and stay the night in Cody.
Day 3 spend day in Yellowstone stay the night in West Yellowstone
Day 4 spend the day in Yellowstone stay the night in Jackson Hole area.
Day 5 Visit the Grand Tetons and maybe start heading back to Denver Maybe stay in Steamboat Springs
day 6 spend day in rmnp also going on trail ridge road stay the night in Estes Park.
Day 7 Head and fly out of Denver to home.

It's still a rough plan we'd explore the towns in the evenings.
Could add 2 days to that if we get more time off.
Is this plan doable? Would it be better to look into Salt Lake City?

One of my favorite Interstate highway section in the US is the stretch from Cove Fort to Grand Junction Co and the rest of I-70 to Denver is pretty awesome. For a field report on this route, take a look at the on-highway options and the off-highway reports.

I think I would choose which city has the best flight plan and price. If you can fly Southwest, you have flexibility to change your mind. Have fun planning your fun trip!