Steve,
As previously noted elsewhere (and here?), if hot springs are the fancy of yourself and Sioux, you can come up US 93 from the Snake River Plain (or down from Missoula) to Gold Bug Hot Springs, just off of US 93 about halfway between Challis and Salmon. It's about a 1 mile hike in (1.5?) and it picks up just over 1,000' elevation, much of it in the last quarter mile. Go as early in the morning as you can, as it starts getting crowded by late morning plus the sun hits it by then, both taking away from an otherwise stellar experience. Got to be some birds around there somewhere, too.
Up in Salmon, there are a number of outfitters and it's a cool hiking/cycling/paddling town, so there MUST be some good eateries.
My GUESS is that Lemhi Pass will be open by late May. It's "only" at about 7,400' so maybe it's open. If not, Bannock Pass should be. It's just under 7,700' but is the crossing of a through-route from Leadore, ID to Dillon, MT.
Over in Dillon is some of the best Mexican fare I've ever had. It's at the Dillon Taco Bus. Located at the north end of Dillon where MT 41 slants away from I-15. There's a large fuel plaza and farm/ranch supply with lots of fishing and camping gear pretty much next to the Taco Bus (Rocky Mountain Supply), so you can get lots of your essentials in one place.
If you cross Lemhi or Bannock pass and want to stay closer to YNP and the ID border, continue on MT 324 to I-15 at Clark Canyon Reservoir or cut south from just east of Grant along the Big Sheep Creek Backcountry Byway. This goes through to Dell, MT about 25 miles north of the ID-MT line on I-15. It stays low so it seems unlikely it'd be closed by snow, although wetness may make it difficult. Either way, head to Lima, MT for an eclectic dining/resupply point which caters to Continental Divide Trail hikers. There are a couple or three cafes in town and the motel offers campsites with electric power.
Check ahead to see if Red Rock Pass is open. If it is, head east from Lima or Monida to run the length of the Centennial Valley to Red Rock Pass. Elevation there just over 7,000' and like Bannock, it's a through-route so seems likely to be open by late May. Just to the north of the grade up to the pass, on the MT side, is Elk Lake Lodge. They're on the Interwebs with what looks like an interesting menu. The Red Rock Lakes NWR is in the heart of the Centennial Valley, as previously discussed.
A drive I'll make one of these days is out Blacktail Creek from Dillon, where it runs +40 miles into and through the Snowcrest Range and ends in the Centennial Valley. If you ended up in Dillon and didn't want to go on I-15 to Lima, you can run out the Blacktail.
I've read that the brother of the Dillon Taco Bus operator has opened a place in Ashton, ID, along the main road from Red Rock Pass to Targhee Pass which then takes you to Jackson, WY just south of YNP.
Foy