There is a pretty good chance that some of the roads will be closed in Yellowstone at that time due to snow. There is also a good chance that you are already to late for lodging. I would stay "in the park" and I would make my reservations ASAP. I would stay @ Jackson Lake Lodge or Colter Village Cabin while in Tetons. Signal Mountain would be nice as well. In Yellowstone -Old faithful Inn and Lake Hotel. I would concentrate you efforts around the Geyser Basin near Old Faithful- See Old Faithful of course, but also see Riverside Geyser and Castle Geyser. See Grand Prismatic Spring and Morning Glory Pool. See some of the mud pots or paint pots. Canyon and Tower areas are great, but this is the spot that I think you might find closed at that time, but it could be open. You may not know until the day you get there. You will want to see the elk around Mammoth Hot Springs. You will want to drive the Lamar Valley(Hayden Valley might be closed). These are the two hot spots for wildlife viewing. Lake Hotel area is interesting for a nights stay. I like Roosevelt Lodge in Yellowstone, but it doesn't open until the 2nd week of June. Take a "yellow bus tour". In Grand Tetons, most everyone hikes to Hidden Falls/Inspiration Point. A float down the Snake River is nice.

At Rushmore, do a wild cave tour in Wind Cave or Jewel cave if you are adventurous.

Highly likely you will see bears when you visit Yellowstone, just take precautions when hiking.

This may not be your last trip- it is that good. You are going at a time when it won't be too busy, say that is a plus as well. Don't let my thoughts about the weather deter you, it will be fantastic. Just wanted you to know that it is pretty likely that some of the roads will be closed. If the Beartooth Hwy is open be sure and drive it.

yellowstone.net is a great blog sight for everything about yellowstone

Gosh where to start. First of all check out the
www. nps.gov/yellowstone web site. It has lots of good information and suggestions -- also Memorial Day is late next year and some of the roads and places to stay within the park won't be open yet when you go. (Canyon doesn't open until June 4 -- not the canyon itself, the lodge). I would probably stay two nights at Old Faithful area and the next two in the northern region (either Mammoth or Gardiner mainly because Dunraven Pass will probably not be open and that will save you some driving while letting you see each area of the park. Make reservations now in the parks -- you can cancel them without penalty if you change your mind (I think it is 48 hours before) but they fill up pretty quick. That is an excellent time to go to see the baby animals, not so great for hiking, but you probably won't be there long enough to do much of that anyway.

If you haven't yet, do some searches here -- there is a ton of information on each park (which can get confusing because there are so many things to do and see and everyone has an opinion on what is a must see). There is no way you can see everything -- the best way to see these parks is to have a loose plan and then be prepared for it to change.

Another good web site to help plan is
http://www.alandsuejohnson.com/.