Depending upon what your interest are I would highly recommend staying in the parks. Yellowstone is a very large park and you may not want to be driving very early or late when it's dark out. Animals on the road could be an issue.

Many people going to these two parks will stay at as many as 3 different places during the visit.

When I was there a couple of years ago we stayed at Old Faithful Loage, Canyon Lodge and Signal Mountail Lodge.

Wildlife is usually around more early and late. If that's of interest.

What general interests do you have. Driving along the roads with sightseeing stops, hiking, photography, etc?

Forgot to mention. Go here: for Yellowstone park lodging:

http://www.yellowstonenationalparklodges.com/

There are a few places in GTNP. We stayed at Signal Mtn.

http://signalmountainlodge.com/

"What general interests do you have. Driving along the roads with sightseeing stops, hiking, photography, etc?"

Mostly the thermal features and wildlife. So it will involve driving around.

Colter Village has some pretty big cabins in The Tetons. I'm not sure about Yellowstone having anything that big.

Call Xanterra for in park lodging - they are very helpful and will guide you in making a selection and letting you know availability. Sometimes a phone call finds more options with availability than the website.
1.866.GEYSERLAND (439-7375)

There are many cabin-type and other lodging in Gardiner, MT, right at the northern entrance (Mammoth Hot Springs area).

http://www.vrbo.com/search/usa/montana/yellowstone/gardiner?sleeps=6-plus

Yellowstone is a very large park.

Also, wildlife are most active early in the morning and early in the evening.

If you are outside the park or even in the park but far from you early or late destinations, you will be driving in the dark. That may not be a good idea with animals possibly on the road.

That's why many people spend time in two areas of Yellowstone and another for Grand Tetons.

As Miami suggested, call Xanterra for options.

Thank you for the tips I will investigate what you have mentioned.

One home base for GTNP and YNP is not practical - and while staying inside National Parks is one experience, there is credible lodging close to several YNP entrances that might serve your groups needs better. About a mile from the entrance to GTNP there is a large complex of condos that are rented out - in all sizes and shapes - with multiple bedrooms, bathrooms and a kitchen if you like. Easy driving distance into Jackson if you want to see anything there.

If the Park lodging for Yellowstone does not work out, I might pick staying in West Yellowstone, MT. While much of the lodging is standard motel, the cost is likely to be much less than lodging for 6 within the Park.

As a certified guide in YNP and vacation rental owner I thought I would assist.
West Yellowstone is the closest entrance to everthing in the Park and you can easily do whole park in day trips from West. You can drive the upper loop one day - the lower loop the next day and then go back and spend more time in areas you liked. You can also go from West to Jackson through the Park and then have lucnha and rive back up through ID (Driggs and Victor) and see the other side of the Tetons. Many like the ID side better.
There are several different types of accomodations available - check out www.YellowstoneWildlifeCabins.com and www.YellowstonePropertyManagement.com to see if any of these interest you.
Remember all accomodations in the park are historical - so pricey and not alot of amentities.

Let meknow if I can help with anything else.

I would definitely stay INSIDE the park. As others have said, call Xanterra to see what is available for your dates.

We'll be heading to GTNP and Yellowstone this fall with 6 adult. Will be staying in West Yellowstone and Jackson Hole. In West Yellowstone, we used
http://letsgotoyellowstone.com/home.html

In Jackson Hole, we used: http://www.mpmjh.com

good luck