arrive mid-day from Montana (could come west entrance
West Yellowstone - Old Faithful (Thermals) Goal to see some of the thermal features on the way to Old Faithful then explore Old Faithful area and boardwalks.
Arrive West Yellowstone ~noonish. Lunch &/or supplies at supermarket. Ideally have a picnic lunch somewhere along the Madison on the way into the park. Depends on when you enter. At Madison Junction turn right, cross the Gibbon river and take the Firehole Canyon Drive. Stop at Fountain Paint Pots then take Firehole Lake Drive. Continue to Old Faithful. Check-in. Find out when Old Faithful's next eruption. (lobbies will all have it noted)
Saturday stay at Old Faithful
Old Faithful-Mammoth (Black Sand, Biscuit, Midway Basins, Fountain Flats, Gibbon Falls, Norris Geyser Basin, Sheepeater cliffs, Mammoth Terraces)
Get an early start and stop at all the stops you didn't on the way in. Picnic lunch either Madison Junction or Gibbon Picnic area. At Norris Junction turn left and visit the Norris Geyser Basin. After turn left(north) Various short roadside stops. Watch for wildlife. Bears good possibility (usually). After Swan Flats you will go through Golden Gate. A short steep section, one turnout on left near top. You will descend toward Mammoth. You can stop at the Mammoth Terraces or continue a short way down to the Mammoth village and come back after you check-in. Explore Mammoth Terraces and Mammoth Village area.
Sunday stay at Mammoth
Mammoth-Lamar-Canyon-Lake Busy day with the most to see and longest distance. 5-7 hours drive time w/o stops depending on how far you go up Lamar valley.
*Ideally* get a early start and go west on the loop road toward Roosevelt Junction to have breakfast at Roosevelt Lodge. Keep a lookout for wildlife, excellent chance of Pronghorn, Elk and even Moose. Look at the Black Canyon of the Yellowstone off to the West. Optional side trip Blacktail Deer Plateau road (NOT IF WET). Short stop at Petrified tree.
After breakfast at take the NE entrance road (left from loop road or straight out of the Roosevelt Lodge drive. Take the road on past the confluence to Soda Butte or Trout Lake or Pebble Creek and turn around and return to junction. You'll have lots of stops to see wildlife. Expect to see people with spotting scopes out in force. Buffalo, pronghorn, wolves, coyotes, fox, raptors maybe more.
After leaving Lamar valley at the junction turn left and continue to Tower Falls. Several overlooks of Grand Canyon of the Yellowstone on way. At Tower Falls you can take the trail/steps to a view of Tower Falls. Reward yourselves with a ice cream.
Continue south over Dunraven Pass. Steep climb winding road up and down with lots of pullouts (one with vault toilets). Keep a sharp eye out going over Dunraven pass on Mount Washburn for wildlife. Best chance to see sheep and mountain goats. Good chance of seeing bears also. Continue on to Canyon Junction. Canyon village is a good rest stop.
Come back to Canyon tomorrow so only one stop. Leave canyon village and turn south(left). Take the turnoff for Artist Point. Pass the north rim and upper falls turnoffs. Take the Artist Paint Point turnoff and drive to the end and check out view after short walk.
Leave Artist Paint Point and turn south(left). Enjoy views of Hayden valley. Lots of chances of wildlife, especially herds of buffalo. Continue on past Fishing Bridge junction to Lake Hotel. Whew, take a well deserved rest.
Monday stay at Lake Hotel
Lake-Canyon-Fishing Bridge-Bridge Bay-Grant
Back to Canyon to see all the viewpoints. Early start improve the chances of seeing wildlife in Hayden valley on the way up. Stop at Brink of Upper Falls. Then continue a short way north to the North rim drive, multiple stops winds back to Canyon Village. The first stop has a path to the brink of the lower falls. Long way down, seems a lot longer back. Not for people with health conditions. But magnificent. There is a path between all the stops for the adventurous and in wonderful shape. I take the car between. Note as you get further away you can see people at the earlier stops. Rest stop at Canyon Village.
Leave Canyon village (south) back to Fishing Bridge Junction turn left (East entrance road). (as always look for wildlife in Hayden valley). Park by bridge and walk out on it and you should see the trout in the river. Might see otters here also. Optional: continue east to Storm Point or even Lake Butte. Wonderful view from Storm Point. Return to Loop road and turn left (south).
When you get to Bridge Bay you can stop, optional: Short hike 1mile to Natural Bridge on old road or Scenic Lake cruise.
After continuing on right(now west) shortly after leaving you have the choice of taking Gull Point Drive. Else continue on to West Thumb Geyser basin. Many lake viewpoints along way. Stop at West Thumb Geyser basin.
After turn left out of parking lot, short distance to West Thumb Junction. Turn left (south) and continue to Grant Village and check-in.
Tuesday stay at Grant Village
If you didn't have time for West Thumb Geyser basin at the end of the previous day backtrack. Else turn south(left) toward Jackson. Stop at Lewis Lake and Lewis Falls. Also wherever strikes your fancy on the way out the park and onto the Tetons.
Wednesday go to Grand Tetons
Thursday return to Montana
Probably more detail than you need initially but give you a good idea what you can do.